Complex Systems Foundations and Applications
Scientific Program
Also: A celebration of the 70th birthday of Constantino Tsallis
CBPF - Rio de Janeiro - Brazil From October 29 to November 1 – 2013 The digital version of this book of abstracts can be downloaded at: http://www.cbpf.br/~compsyst/index.php Cover photo: C. Tsallis in his CBPF office, 2013, Rio de Janeiro, Brazil. Credits: J. Ricardo. Foreword
Dear Colleagues,
We are very pleased to meet you here in CBPF, Rio de Janeiro, for the Complex Systems – Foundations and Applications conference. This will be an international event covering many topics in the area of complex systems, like nonlinear phenomena, econophysics, foundations and ap- plications of non-extensive statistical mechanics, biological complexity, far-from-equilibrium phenomena, nonequilibrium in social and natural sciences, and interdisciplinary applications, among others. In this event, we will also celebrate the 70th birthday of Constantino Tsallis.
We wish you all a great conference.
Andr´eM. C. Souza (UFS) Evaldo M. F. Curado (CBPF) Fernando D. Nobre (CBPF) Roberto F. S. Andrade (UFBA)
ORGANIZING COMMITTEE Scientific Program
DAY I DAY II DAY III DAY IV TUESDAY WEDNESDAY THURSDAY FRIDAY 29/10/2013 30/10/2013 31/10/2013 01/11/2013 08h00 – 09h00 Registration
09h00 – 09h30 Opening ORAL COMMUNICATIONS
09h30 – 10h30 ORAL COMMUNICATIONS
10h30 – 11h00 Coffee Break
11h00 – 12h30 ORAL COMMUNICATIONS
12h30 – 14h30 LUNCH
14h30 – 16h00 ORAL COMMUNICATIONS
16h00 – 16h30 Coffee Break Coffee Break and Coffee Break
16h30 – 17h00 ORAL COM. POSTER SESSIONS‡ ORAL COM.
17h00 – 17h30 ORAL COMMUNICATIONS C. TSALLIS ORAL COM.
17h30 – 18h00 ORAL COMMUNICATIONS SPECIAL Closure
18h00 – 18h30 Cocktail TALK
20h00 Dinner
All talks: 25 minutes (presentation) + 5 minutes (questions).
‡Posters should be fixed before the morning section ( 8:30 a.m.) ∼ and removed at the end of each day. Scientific Program 5
DAY I DAY II DAY III DAY IV TUESDAY WEDNESDAY THURSDAY FRIDAY 29/10/2013 30/10/2013 31/10/2013 01/11/2013 08h00 – 09h00 Registration
09h00 – 09h30 Opening S. Canuto H. J. Jensen R. Dickman
09h30 – 10h00 H. Herrmann A. Deppman J. Naudts R. Maynard
10h00 – 10h30 B. Cabral A. R. Plastino S. Umarov F. L. Ribeiro
10h30 – 11h00 Coffee Break
11h00 – 11h30 U. Tirnakli A. Pluchino P. Bourgine S. Thurner
11h30 – 12h00 H. Suyari S. D. Queir´os N. Kalogeropoulos R. Hanel
12h00 – 12h30 A. S. Martinez L. S. Lucena J. S. Dehesa A. Morais
12h30 – 14h30 LUNCH
14h30 – 15h00 J. S. Andrade A. Coniglio R. Rossignoli S. C. Ferreira
15h00 – 15h30 L. R. da Silva G. P. Pavlos R. S. Mendes G. Ruiz
15h30 – 16h00 M. B. Ribeiro L. Karakatsanis R. Riera O. A. Rosso
16h00 – 16h30 Coffee Break Coffee Break and Coffee Break
16h30 – 17h00 A. Rapisarda POSTER SESSIONS‡ R. Wedemann
17h00 – 17h30 A. R. Mesas A. Robledo C. TSALLIS M. Barbosa
17h30 – 18h00 E. E. Vogel G. C. Yalcin SPECIAL Closure
18h00 – 18h30 Cocktail TALK
20h00 Dinner
All talks: 25 minutes (presentation) + 5 minutes (questions).
‡Posters should be fixed before the morning section ( 8:30 a.m.) ∼ and removed at the end of each day. Program: Oral Communications 6
Day I – Tuesday – 29/10/2013
08:00h Registration 09:00h Opening: Fernando L. Freire J´unior & Fernando D. Nobre Oral Communications Morning I Chair: Fernando D. Nobre
09:30h Hans Herrmann – ETH Zurich/Switzerland¨ & UFC/Cear´a/Brazil Fluids in curved space ...... 34 10:00h Benedito J. C. Cabral – ULisboa/Lisboa/Portugal Hydrogen bond networks and electronic properties of complex systems...... 27
10:30h Coffee Break
Oral Communications Morning II Chair: Roberto F. S. Andrade
11:00h Ugur Tirnakli – Ege University/Izmir/Turkey˙ Central limit behaviour of dynamical systems: Emergence of q-Gaussians and scaling laws ...... 59 11:30h Hiroki Suyari – Chiba University/Japan Combinatorial basis for Tsallis entropy and its applications ...... 36 12:00h Alexandre Souto Martinez – USP/S˜ao Paulo/Brazil Ergodic transition in partially self-avoiding stochastic walks ...... 21
12:30h LUNCH
Oral Communications Afternoon I Chair: Roger Maynard
14:30h Jos´eSoares de Andrade Jr. – UFC/Cear´a/Brazil Optimal synchronizability of bearings ...... 38
continue on next page Program: Oral Communications 7
Day I – Tuesday – 29/10/2013
15:00h Luciano R. da Silva – UFRN/Rio Grande do Norte/Brazil The general preferential attachment growth model and nonextensive statistical mechanics ...... 41 15:30h Marcelo B. Ribeiro – UFRJ/Rio de Janeiro/Brazil Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil ...... 43
16:00h Coffee Break
Oral Communications Afternoon II Chair: Celia B. Anteneodo
16:30h Andrea Rapisarda – UNICT/Catania/Italy The beneficial role of random strategies in social and financial complex systems ...... 23 17:00h Antonio Rodr´ıguez Mesas – UPM/Madrid/Spain A scale-invariant probabilistic model based on Leibniz-like pyramids ... 25 17:30h Eugenio E. Vogel – UFRO/Temuco/Chile Stock market variations by means of information theory ...... 28
18:00h Cocktail Program: Oral Communications 8
Day II – Wednesday – 30/10/2013
Oral Communications Morning I Chair: Stefan Thurner
09:00h Sylvio Canuto – USP/S˜ao Paulo/Brazil Dielectric constant at the critical point ...... 59 09:30h Airton Deppman – USP/S˜ao Paulo/Brazil Non-extensive self-consistency in hadronic medium ...... 18
10:00h Angel Ricardo Plastino – UNNOBA/Buenos Aires/Argentina Aspects of the NRT nonlinear Schroedinger equation...... 24
10:30h Coffee Break
Oral Communications Morning II Chair: Andrea Rapisarda
11:00h Alessandro Pluchino – UNICT/Catania/Italy Noise, synchrony and correlations at the edge of chaos ...... 20 11:30h S´ılvio M. Duarte Queir´os – CBPF/Rio de Janeiro/Brazil On generalisations of the log-Normal distribution by means of a new product definition in the Kapteyn process...... 57 12:00h Liacir dos Santos Lucena – UFRN/Rio Grande do Norte/Brazil Wavelet coherency in complex systems ...... 40
12:30h LUNCH
Oral Communications Afternoon I Chair: Henrik J. Jensen
14:30h Antonio Coniglio – Univ. of Naples “Federico II”/Italy Cell theory for the glass transition...... 25
continue on next page Program: Oral Communications 9
Day II – Wednesday – 30/10/2013
15:00h Georgios P. Pavlos – DUTH/Thrace/Greece Universality of Tsallis non-extensive statistics and time series analysis: Theory and applications ...... 30 15:30h Leonidas P. Karakatsanis – DUTH/Thrace/Greece Earth’s climate complexity ...... 39
16:00h Coffee Break and POSTER SESSION
Oral Communications Afternoon II Chair: Allbens P. F. Atman
17:00h Alberto Robledo – UNAM/Mexico City/Mexico Incidence of Tsallis statistics in rank distributions ...... 19 17:30h G. Cigdem Yalcin – Istanbul University/Turkey Environmental aspects of superstatistics: Temperature ...... 33 Program: Oral Communications 10
Day III – Thursday – 31/10/2013
Oral Communications Morning I Chair: Jeferson J. Arenzon
09:00h Henrik Jeldtoft Jensen – Imperial College London/UK Restricted random walk model as a new testing ground for the applicability of q-statistics ...... 35 09:30h Jan Naudts – University of Antwerp/Belgium Statistical mechanics from the point of view of information geometry ...... 37
10:00h Sabir Umarov – UNH/Connecticut/United States Beyond the triangle – Brownian motion, Itˆostochastic calculus, and Fokker-Planck equation: fractional generalizations ...... 54
10:30h Coffee Break
Oral Communications Morning II Chair: Angel R. Plastino
11:00h Paul Bourgine – Ecole´ Polytechnique/Paris/France Phenomenological and theoretical reconstruction in the framework of information geometry science is the process of reconstructing theory from data...... 46 11:30h Nikos Kalogeropoulos – WCMC-Q/Doha/Qatar Tsallis entropy composition: a geometric view ...... 44 12:00h Jes´us S´anchez-Dehesa – UGR/Granada/Spain Tsallis’ entropy for central potentials: Improved bounds and uncertainty relations...... 38
12:30h LUNCH
continue on next page Program: Oral Communications 11
Day III – Thursday – 31/10/2013
Oral Communications Afternoon Chair: Marcia C. Barbosa
14:30h Ra´ul Rossignoli – UNLP/La Plata/Argentina Generalized entropic measures of quantum correlations ...... 47 15:00h Renio dos Santos Mendes – UEM/Paran´a/Brazil Data analysis of elections ...... 48 15:30h Rosane Riera – PUC-Rio/Rio de Janeiro/Brazil An Information-based tool for inferring the nature of deterministic sources in real data ...... 50
16:00h Coffee Break and POSTER SESSION
Special Talk Chair: Evaldo M. F. Curado
17:00h Constantino Tsallis – CBPF/RJ/Brazil & SFI/New Mexico/USA Theoretical physics: Crossroads of truth and beauty ...... 28
20:00h Dinner Program: Oral Communications 12
Day IV – Friday – 01/11/2013
Oral Communications Morning I Chair: Jos´eS. Andrade Jr.
09:00h Ronald Dickman – UFMG/Minas Gerais/Brazil The Cancho i Ferrer - Sol´emodel does not explain Zipf’s Law ...... 49 09:30h Roger Maynard – UJF/Grenoble/France Imaging in complex media: Recent progresses...... 49
10:00h Fabiano Lemes Ribeiro – UFLA/Minas Gerais/Brazil A non-phenomenological model to explain population growth behaviors ...... 29
10:30h Coffee Break
Oral Communications Morning II Chair: Benedito Cabral
11:00h Stefan Thurner – MUV/Vienna/Austria Entropy for complex and non-ergodic systems, a derivation from first principles ...... 57 11:30h Rudolf Hanel – MUV/Vienna/Austria From multiplicity to entropy ...... 51 12:00h Apiano Morais – URCA/Cear´a/Brazil Self-organised fractal corrosion in heterogeneous solids ...... 26
12:30h LUNCH
Oral Communications Afternoon I Chair: Ronald Dickman
14:30h S´ılvio C. Ferreira – UFV/Minas Gerais/Brazil Mean-field theories and quasi-stationary simulations of epidemics models on complex networks ...... 56
continue on next page Program: Oral Communications 13
Day IV – Friday – 01/11/2013
15:00h Guiomar Ruiz Lopez – UPM/Madrid/Spain Towards a large deviation theory for statistical-mechanical complex systems...... 32 15:30h Osvaldo A. Rosso – UFAL/Alagoas/Brazil & UBA/B. Aires/Argentina Distinguishing noise from chaos: an Information Theory approach.....45
16:00h Coffee Break
Oral Communications Afternoon II Chair: Ugur Tirnakli
16:30h Roseli S. Wedemann – UERJ/Rio de Janeiro/Brazil Some properties of memory retrieval in an associative memory neural net- work for conscious and unconscious mental behavior ...... 52 17:00h Marcia C. Barbosa – UFRGS/Rio Grande do Sul/Brazil Enhancement flow in nanoconfined water ...... 44
17:30h Closure Program: Poster Sessions 14
POSTER SESSION
Day II – Wednesday – 30/10/2013
Chair: Luciana A. Rios
01 Alyson Paulo Santos – UFRN/Rio Grande do Norte/Brazil Non extensive H-Theorem in General Relativity ...... 62
02 Andres M. Kowalski – UNLP/La Plata/Argentina Generalized complexity and classical-quantum transition...... 62
03 Angel Akio Tateishi – UEM/Paran´a/Brazil The transformation groupoid structure of the q-Gaussian family ...... 63
04 Bruno G. da Costa – IFSert˜ao-PE/Pernambuco/Brazil Classical and quantum harmonic oscillator with position-dependent mass...64
05 Cesar Ivan Nunes Sampaio Filho – UFC/Cear´a/Brazil Scaling functions for systems with finite range of interaction ...... 65
06 Daniel Brito de Freitas – UFRN/Rio Grande do Norte/Brazil A nonextensive approach to the stellar rotational evolution for F- and G-type stars ...... 66
07 Diego Mateos – UNC/C´ordoba/Argentina A Comparison between methods for analyzing physiological time series.....66
08 Edson P. da Silva – UFRRJ/Rio de Janeiro/Brazil A Kramers-Moyal expansion approach to time series of the atmospheric tem- perature – A contribution to the discussion of the global weather change...68
09 Ernesto P. Borges – UFBA/Bahia/Brazil Generalized space and linear momentum operators in quantum mechanics .. 69
10 Ervin K. Lenzi – UEM/Paran´a/Brazil Fractional diffusion equation, surface effects and anomalous diffusion ...... 70
11 Felipe Aguiar Severino dos Santos – UFOP/Minas Gerais/Brazil Scaling exponents of rough surfaces generated by damage spreading in the Ising model ...... 70 Program: Poster Sessions 15
12 Felipe Olivares – UNLP/La Plata/Argentina Permutation quantifiers and the fine structure on the chaotic attractors. ... 71
13 Fernando J. Antˆonio – UEM/Paran´a/Brazil Growing jackpot and persistence in lottery winners...... 74
14 Fl´avio S. Michels – UEM/Paran´a/Brazil First passage time for a diffusive process under a geometric constraint ..... 74
15 Fortunato Silva de Menezes – UFLA/Minas Gerais/Brazil Alternative measures for biospeckle image analysis ...... 75
16 Francisco Rocha – UFPE/Pernambuco/Brazil Control of centrifugal fingering via a variable interfacial tension approach .. 76
17 Gabriel Dias Carvalho – UFPE/Pernambuco/Brazil Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study ... 76
18 Gabriela A. Casas – CBPF/Rio de Janeiro/Brazil Entropy Production in systems described by a master equation ...... 77
19 Jo˜ao V. Fontana – UFPE/Pernambuco/Brazil Radial viscous fingering in yield stress fluids: Onset of pattern formation ... 78
20 Jos´eA. C. Nogales & Karen Burgoa-Rosso – UFLA/Minas Gerais/Brazil Nonextensive thermostatistic properties of compact stars ...... 78
21 Jos´eWeberszpil – UFRRJ/Rio de Janeiro/Brazil Anomalous g-factors for charged leptons in a fractional coarse-grained approach ...... 79
22 Leandro Prade Nadaletti – COPPE/UFRJ/Rio de Janeiro/Brazil Synchronization as a mechanism for protein folding ...... 81
23 Marco A. Rego Monteiro – CBPF/Rio de Janeiro/Brazil Classical field theory for a nonlinear Schroedinger equation ...... 86
24 Reinaldo R. Rosa – INPE/S˜ao Paulo/Brazil Statistical complexity and pattern formation in cosmology...... 91 Program: Poster Sessions 16
POSTER SESSION
Day III – Thursday – 31/10/2013
Chair: Ernesto P. Borges
01 Allbens P. F. Atman – CEFET-MG/Minas Gerais/Brazil Non-Gaussian behavior in jamming / unjamming transition in dense granular materials...... 61
02 Elton Jos´eda Silva J´unior – UFMG/Minas Gerais/Brazil Reactive strategies: The establishment of cooperation ...... 68
03 Felipe Mondaini – CEFET-RJ/Rio de Janeiro/Brazil Free energy evaluation in polymer translocation via Jarzynski equality...... 73
04 Leonardo J. L. Cirto – CBPF/Rio de Janeiro/Brazil Controlling the range of interactions in the classical inertial Heisenberg model ...... 80
05 Luciana A. Rios – CBPF/Rio de Janeiro/Brazil Ion-acoustic double-layers in magnetized plasmas with nonthermal electrons ...... 83
06 Luiz G. A. Alves – UEM/Paran´a/Brazil Scaling laws in the dynamics of crime growth rate ...... 84
07 Mauricio S. Ribeiro – CBPF/Rio de Janeiro/Brazil Overdamped motion of interacting particles in general confining potentials: Time-dependent and stationary-state analyses ...... 87
08 Maike A. F. dos Santos – UEM/Paran´a/Brazil Nonlinear diffusion equation, solutions and Tsallis framework ...... 85
09 Marcelo L. Martins – UFV/Minas Gerais/Brazil Boolean network model for cancer pathways: predicting carcinogenesis and target therapy outcomes ...... 85
10 Maury Duarte Correia – CBPF/PETROBRAS/Rio de Janeiro/Brazil q-Statistics modelling NMR decay of unconsolidated porous media...... 88 Program: Poster Sessions 17
11 Max J´auregui – CBPF/Rio de Janeiro/Brazil A representation of the Dirac delta based on the q-exponential function....88 12 Norma Canosa – UNLP/La Plata/Argentina Generalized information deficit and quantum discord in spin chains ...... 89
13 Pablo de Castro – UFPE/Pernambuco/Brazil Role of viscous friction in the reverse rotation of a disk ...... 90
14 Rebeca C. Falc˜ao – UFPE/Pernambuco/Brazil Statistical model of impact fragmentation in a disk ...... 91
15 Renato R. Guimar˜aes – UEM/Paran´a/Brazil Scaling law and anti-persistent motion of annihilating defects in a lyotropic liquid crystal...... 92
16 Roberto da Silva – UFRGS/Rio Grande do Sul/Brazil Time-dependent Monte Carlo simulations for the refinement of critical points for extensive and non-extensive spin models...... 93
17 Sabrina Camargo – EMAp/FGV/Rio de Janeiro/Brazil Bridging stylized facts in finance and data non-stationarities...... 94
18 Sergio Curilef – UCN/Antofagasta/Chile Analytical solutions for a nonlinear diffusion equation: convection and reaction terms ...... 95
19 Steeve Zozor – GIPSA-Lab/Grenoble/France & UNLP/La Plata/Argentina On generalized entropic uncertainty relations for the quNit ...... 95
20 Suani T. R. Pinho – UFBA/Bahia/Brazil Deformed Pythagorean triples and Fibonacci sequences ...... 97
21 Thierry C. Petit Lob˜ao – UFBA/Bahia/Brazil A family of Leibniz triangles as models for correlated systems ...... 98
22 Victor Pedrosa – UFPE/Pernambuco/Brazil Electronic transport through disordered wires using Stochastic Differential Equations ...... 99
23 Wellington P. A. Spinola – UFOP/Minas Gerais/Brazil Cellular Automata simulation of people moving in confined space in the presence of obstacles ...... 100 Abstracts: Oral Communications
Non-extensive self-consistency in hadronic medium Airton Deppman Universidade de S˜ao Paulo (USP) – S˜ao Paulo – Brazil The high energy experiments have provided us with many data which has confirmed that a tail-like distribution, as that which follows from the Tsallis statistics, can describe the transversal momentum, pT , distribu- tions. Nonetheless, the use of non-extensive statistics remains a rather controversial subject. The non-extensive self-consistent theory recently proposed [1] predicts that hot hadronic matter should present a limiting effective temperature and a limiting entropic index. Also, it predicts that the pT -distribution at high energy collision should be described by the expression
q d2N p m cosh y m cosh y µ − q−1 = gV T T 1+(q 1) T − , (1) dp dy (2π)2 − T T which is somewhat different from the most used expression for fitting experimental data [2], and that the cumulative hadron mass spectrum should be given by [3]
m r(m)= ρ(m′)dm′ = Zo (2) 2γ 3/2 3 1 1 = − m− F , ; ; (q 1)βm + k. 3 2 1 − 2 −q 1 −2 − − − It will be shown that existing experimental data for pT distributions and for observed hadron states give support to the theory [4], and there- fore show that the non-extensivity passes the restrictive test mentioned above. With these results one can obtain a complete description of the thermodynamics for hadronic systems at high temperatures. Some ther- modynamical functions are calculated and compared with lattice-QCD results. Abstracts: Oral Communications 19
Figure 1: Effective temperature, T , resulting from the fittings of Eq. (1) (full symbols) and from the usual expression for fittings [2] (open symbols). The inset shows the effective temperature obtained through the use of Eq.(1) in more details. Full lines indicate the constant value, To, which best fits the data obtained with Eq. (1) assuming y = 0 and µ = 0.
[1] A. Deppman, Physica A 391 6380–6385 (2012); [2] J. Cleymans, D. Worku, J. Phys. G: Nucl. Part. Phys. 39, 025006 (2012); [3] L. Marques, E. Andrade-II, A. Deppman, arXiv:1210.1725; [4] I. Sena, A. Deppman, accepted for publication in Eur. Phys. J. A (2013) – arXiv:1208.2952v1. Email address: [email protected].
Incidence of Tsallis statistics in rank distributions
1 2, G. Cigdem Yalcin & Alberto Robledo † 1Department of Physics, Istanbul University – Istanbul – Turkey 2Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico (UNAM) – Ciudad de M´exico – Mexico We show that both size-rank and frequency-rank distributions observed in a limitless number of instances in a widespread family of systems, as- Abstracts: Oral Communications 20 trophysical, geophysical, ecological, biological, technological, urban, so- cial, and human, obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or van- ishes. The relevant statistical-mechanical expressions are derived from a maximum entropy principle and the resulting duality of entropy indexes is seen to portray physically relevant information. †Email address: rob- [email protected].
Noise, synchrony and correlations at the edge of chaos Alessandro Pluchino1,2 & Andrea Rapisarda1,2 & Constantino Tsallis2,3 1Dipart. di Fisica e Astronomia, Universit`adi Catania (UNICT) & INFN sezione di Catania – Catania – Italy 2Centro Brasileiro de Pesquisas Fisicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil 3Santa Fe Institute (SFI) – New Mexico – USA Since the nonlinear phenomenon of synchronization was first observed and discussed in the 17th century by Huygens, it has become of fun- damental importance in various fields of science and engineering. It is frequently observed in complex systems such as biological ones, or single cells, physiological systems, organisms and even populations. Synchrony among coupled units has been extensively studied in the past decades providing important insights on the mechanisms that generate such an emergent collective behavior [1,2,3]. In this context coupled maps have often been used as a theoretical model [4]. Actually, many biological complex systems operate in a noisy environment and most likely at the edge of chaos [5]. Therefore studying the effect of a weak noise in this kind of coupled systems could be relevant in order to understand the way in which interacting units behave in rea l complex systems like for example living cells [6,7]. In previous studies [8,9] the effect of a small noise on globally coupled chaotic units was presented for several kind of systems and a universal behavior related to the Lyapunov spectrum was found to be a common feature. Power-law correlations and intermittent behavior have also been observed in lattices of logistic maps when some Abstracts: Oral Communications 21 kind of global coupling exist among them [10,11]. In this talk we con- sider the effect of a weak random additive noise in a linear chain of N locally-coupled logistic maps at the edge of chaos [12]. Maps tend to syn- chronize for a strong enough coupling, but if a weak noise is added, very intermittent fluctuations in the returns time series are observed. This in- termittency tends to disappear when noise is increased. Considering the pdfs of the returns, we observe the emergence of fat tails which can be satisfactorily reproduced by q-Gaussians curves typical of nonextensive statistical mechanics. Interoccurrence times of these extreme events are also studied in detail. Similarities with recent analysis of financial data are also discussed. [1] S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order, (Hy- perion Books, 2004); [2] A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization. A Universal Con- cept in Nonlinear Sciences, (Cambridge University Press, Cambridge, 2001); [3] Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, (Springer, New York, 1984); [4] K. Kaneko, Simulating Physics with Coupled Map Lattices, (World Scien- tific, Singapore, 1990); [5] C. Langton, Physica D 42, 12 (1990); [6] D. Stokic, R. Hanel, S. Thurner, Phys. Rev. E. 77, 061917 (2008); [7] R. Hanel, M. P¨ochacker, M. Sch¨olling, S.Thurner, Plos One 7, e36679 (2012); [8] T. Shibata, T. Chawanya and K. Kaneko, Phys. Rev. Lett. 82, 4424 (1999); [9] J. Teramae, Y. Kuramoto, Phys. Rev. E 60, 036210 (2001); [10] N.B. Ouchi, K. Kaneko, Chaos 10, 359 (2000); [11] C. Li, J. Fang, IEEE 0-7803-8834-8/05 (2005); [12] A. Pluchino, A. Rapisarda, C. Tsallis, Phys. Rev. E 87, 022910 (2013).
Ergodic transition in partially self-avoiding stochastic walks Juliana M. Berbert & Rodrigo S. Gonzalez & Alexandre S. Martinez Universidade de S˜ao Paulo (USP) – S˜ao Paulo – Brazil Consider a one-dimensional environment with N randomly distributed sites. An agent explores this random medium moving deterministically Abstracts: Oral Communications 22 with a spatial memory µ. A transition from local to global exploration is present at a well-defined memory value µ1 = log2 N. In its stochastic version, the dynamics is ruled by the memory and also by temperature T , which affects the hopping displacement. This dynamics also shows a transition, obtained computationally, between exploration schemes, char- acterized yet, by the trajectory size (Np) (aging effect). For an analytical approach, we consider the modified stochastic version in d dimensions, where the parameter T plays the role of a maximum hopping distance. This modification allows us to obtain a general analytical expression for the transition, as function of the parameters µ, T and Np. These results have been validated by numerical experiments and may be of great use fixing optimal parameters in search algorithms.
Coin state properties in quantum walks
Andr´eM. C. Souza1,3 & Roberto F. S. Andrade2,3 1Universidade Federal de Sergipe (UFS) – Sergipe – Brazil 2Universidade Federal da Bahia (UFBA) – Bahia – Brazil 3National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil Recent experimental advances have measured individual coin components in discrete time quantum walks, which have not received the due atten- tion in most of the theoretical studies on the theme. Properties of M, the difference between square modulus of coins states are investigated for a particle undergoing a discrete walk on a finite linear chain. Local ex- pectation values are evaluated in terms of the real and imaginary part of the Fourier transformed wave function. A simple expression is found for the average difference between coin states in terms of an angle θ gauging the coin operator and its initial state. These results are corroborated by the numerical integration of the dynamical equations in real space. The local dependence is characterized both by large and short period modu- lations. The richness of the revealed patterns suggests that the amount of information stored and retrieved from quantum walks is signicantly enhanced if M is taken into account. Abstracts: Oral Communications 23 The beneficial role of random strategies in social and financial complex systems
Alessio Emanuele Biondo1 & Alessandro Pluchino2 & Andrea Rapisarda2 & Dirk Helbing3 1Dipart. di Economia e Impresa, Universit´adi Catania (UNICT) – Catania – Italy 2Dipart. di Fisica e Astronomia, Universit`adi Catania (UNICT) & INFN sezione di Catania – Catania – Italy 3Eidgen¨ossische Technische Hochschule Zurich¨ (ETH Zurich)¨ – Zurich¨ – Switzerland
In physics, noise and randomness are usually restricted to be as low as possible in order to avoid any influence on the phenomena under exam- ination. Actually, this is not often possible and one has to live with noise, but, random noise is not always so annoying as one might think intuitively. In fact there are many examples where randomness has been proven to be extremely useful and beneficial. On the other hand, in the last years, there has been an increasing interest in social complex phe- nomena by the physics community. In this talk we focus our attention on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review re- cent results obtained by two of us in previous contributions for the case of the Peter principle [1,2] and the efficiency of a Parliament [3]. Then, we address a new application of random strategies to the case of financial trading and dis cuss in detail our findings about markets dynamics. Our results clearly show that the performance of random strategies in pre- dicting the evolution of the markets is, on average and in the long term, quite similar to that of traditional approaches, but its variability on a small time scale is much lower. On the other hand, random strategies, used not only at an individual level but also at a global scale, may also be able to avoid herding effects among investors and, consequently, can reduce the probability of dangerous “avalanche effects” that have been among the main causes of the dramatic recent collapses of financial mar- kets [4,5]. [1] A. Pluchino, A. Rapisarda, C. Garofalo, The Peter principle revisited: a computational study, Physica A 389, 467 (2010), see also http://oldweb.ct.infn.it/cactus/peter-links.html; Abstracts: Oral Communications 24
[2] A. Pluchino, A. Rapisarda, C. Garofalo, Efficient promotion strategies in hierarchical organizations, Physica A 390, 3496 (2011); [3] A. Pluchino, C. Garofalo, A. Rapisarda, S. Spagano, M. Caserta, Acci- dental politicians: how randomly selected legislators can improve Parliament efficiency, Physica A 390, 3944 (2011), see also http://www.pluchino.it/Parliament.html; [4] A. E. Biondo, A. Pluchino, A. Rapisarda, The beneficial role of random strategies in social and financial systems, J. Stat. Phys, 151, 607 (2013); [5] A. E. Biondo, A. Pluchino, A. Rapisarda, D. Helbing, Are random trad- ing strategies more successful than technical ones?, PLOS ONE 8(7), e68344 (2013), see also http://www.pluchino.it/financial-markets.html.
MaxEnt and von Bertalanffy’s growth processes
Angel Plastino Universidad Nacional de La Plata (UNLP) – La Plata – Argentina
In this communication show how to introduce dynamical information into the MaxEnt principle so as to deal with von Bertalanffy’s growth processes, thus extending results concerning power-laws with exponential cutoffs. von Bertalanffy’s is the most widely used growth curve, being especially important in fisheries studies.
Aspects of the NRT nonlinear Schroedinger equation
Angel Ricardo Plastino Universidad Nacional Noroeste (UNNOBA) – Buenos Aires – Argentina
We explore various aspects of the nonlinear Schrodinger equation recently advanced by Nobre, Regio-Montero, and Tsallis (NRT), based on Tsallis q-thermo-statistical formalism. We investigate some symmetries of this equation, leading to new analytical solutions. A pilot-wave approach to the NRT equation is also discussed. Abstracts: Oral Communications 25
Cell theory for the glass transition
Antonio Coniglio University of Naples“Federico II”– Naples – Italy
Many theories have been proposed in the past years to explain the phe- nomenology associated to the glass transition. These include, among others, the free volume theory, the cooperative rearranging regions, the mode coupling theory, inherent structures, random first order transitions. These theories are not necessarily in contradiction with each other, but each catches some aspect of the glass transition. Here I will present a new approach, recently developed with Tomaso Aste, that combines some ideas of these previous theories, together with new concepts, originally introduced by Costantino Tsallis in his novel extension of the statistical mechanics entropy. The consequences of the theory will be discussed and compared with experimental and numerical results.
A scale-invariant probabilistic model based on Leibniz-like pyramids
Antonio Rodr´ıguez Mesas1 & Constantino Tsallis2 1Dpto. de Matem´atica Aplicada y Estad´ıstica, Universidad Polit´ecnica de Madrid (UPM) – Madrid – Spain 2Centro Brasileiro de Pesquisas F´ısicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil
We introduce a family of probabilistic scale-invariant Leibniz-like pyra- mids and (d)-dimensional hyperpyramids (d = 1, 2, 3,...), with d = 1 corresponding to triangles, d = 2 to (tetrahedral) pyramids, and so on. For all values of d, they are characterized by a parameter ν > 0, whose value determines the degree of correlation between N (d)-valued random variables (d = 1 corresponds to binary variables, d = 2 to ternary vari- ables, and so on). There are (d)N different events, and the limit ν corresponds to independent random variables, in which case each→ event ∞ Abstracts: Oral Communications 26 has a probability 1/(d)N to occur. The sums of these N (d)-valued ran- dom variables correspond to a d dimensional probabilistic model, and generalizes a recently proposed one-dimensional− (d = 1) model having q Gaussians (with q =(ν 2)/(ν 1) for ν [1, )) as N limit probability− distributions for− the sum− of the N∈ binary∞ variables→ ∞ [A. Ro- dr´ıguez et al, J. Stat. Mech. P09006 (2008); R. Hanel et al, Eur. Phys. J. B 72, 263 (2009)]. In the ν limit the d dimensional multinomial distribution is recovered for the→ ∞ sums, which approach− a d dimensional Gaussian distribution for N . For any ν, the conditional− distribu- tions of the d dimensional model→ ∞ are shown to yield the corresponding joint distribution− of the (d 1)-dimensional model with the same ν. For the d = 2 case, we study the− joint probability distribution, and identify two classes of marginal distributions, one of them being asymmetric and scale-invariant, while the other one is symmetric and only asymptotically scale-invariant. The present probabilistic model is proposed as a testing ground for a deeper understanding of the necessary and sufficient condi- tions for having q-Gaussian attractors in the N limit, the ultimate goal being a neat mathematical view of the causes→ ∞ clarifying the ubiq- uitous emergence of q-statistics verified in many natural, artificial and social systems.
Self-organised fractal corrosion in heterogeneous solids
Apiano Morais Universidade Regional do Cariri (URCA) – Cear´a– Brazil
In this study I investigated through a new mathematical model and com- puter simulations the generalized corrosion process in which a solid is in contact with an agressive solution. In this model the solid is identified in a rectangular lattice with L sites in width and infinity in length, with periodic conditions in width. Each site is assigned a property of resis- tance to corrosion r that in this work is distributed randomly [0, 1], where the unitary value stands for maximum resistance. In an initial step the agressive particles, Q, of the solution are distributed over a volume V0 and I assume the agressiveness p is proportional to the concentration of Abstracts: Oral Communications 27 particles. The portion of the solid in contact with the solution may be corroded if p (t) > ri. As many sites are corroded the volume of the solution increases and the concetration decreases. The agressiveness is 1 γ − obtained as p (t) 1 L N (t) with N standing for the number of cor- roded sites. The≡ dynamics of the system evolves until a spontaneous stop. An infinity cluster emerges and we identify it as the final corrosion front. The final fronts present fractal dimensions in the range 1.33 to 1.75. The average width of the final front depends on γ in a power-law fashion, as well as the final agressiveness. Also, we found a hardening of the final front as γ decreases.
Hydrogen bond networks and electronic properties of complex systems
Benedito J. C. Cabral† Grupo de F´ısica Matem´atica, Universidade de Lisboa (ULisboa) – Lisboa – Portugal The structure and electronic properties of the hydrogen bond (HB) net- works of polar liquids are investigated by carrying out sequential quantum mechanics/Born-Oppenheimer molecular dynamics (BOMD). Emphasis is placed on liquid hydrogen fluoride (HF) [1] and hydrogen cyanide (HCN) [2]. These systems may form HB networks with a rich topo- logical structure consisting of polymerized chains, ramified, and cyclic aggregates. HCN is also a prebiotic and extraterrestrial species closely related to the origin of life. The theoretical approach relies on the cal- culation of the electronic properties using configurations generated by BOMD. We put some emphasis on the possibility to carry out ab initio calculations for the electronic properties in the liquid phase by coupling many-body energy decomposition schemes [3] to BOMD configurations. [1] B. J. C. Cabral, K. Coutinho, S. Canuto, Chem. Phys. Lett. 495, 40 (2010); [2] H. F. M. C. Martiniano, B. J. C. Cabral, Chem. Phys. Lett. 55, 119 (2013); [3] R. A. Mata, B. J. C. Cabral, Adv. Quantum Chem. 59, 99 (2010). †Pesquisador Visitante, Instituto de F´ısica da Universidade de S˜ao Paulo (USP), S˜ao Paulo, Brazil. Abstracts: Oral Communications 28
Theoretical physics: Crossroads of truth and beauty Constantino Tsallis Centro Brasileiro de Pesquisas F´ısicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil Santa Fe Institute (SFI) – New Mexico – USA
Stock market variations by means of information theory
Eugenio E. Vogel† & G. Saravia Depto. Ciencias F´ısicas, Universidad de La Frontera (UFRO) – Temuco – Chile Information theory has proven to be useful to understand different phe- nomena. In particular data compressor techniques have allowed to rec- ognize and characterize magnetic transitions [1]. In the present con- tribution we consider the use of these techniques in econophysics, to explore the variations, or degree of agitation, of the stock markets in- dicators showing that information theory can help to recognize different regimes. Actually the onset of the different regimes can be established after some time measured in minutes which could allow to prevent ex- treme loses in the market. We begin by introducing improvements to data compressor wlzip reported in the reference above. On one hand, we recognize that wlzip allows for two different and simultaneous mea- surements: a) diversity, which accounts for the number of visited states during the evolution of the system in any time window; b) mutability, which measures the agitation of the system changing among the possi- ble states. On the other hand we introduce a mechanism for rounding off truncations while doing the compression which allows to concentrate on the significant digits for each different application. We illustrate the technique with the well known ferromagnetic to paramagnetic transitions of the Edwards-Anderson model in 2D and in 3D. Then we move onto the main Chilean stock market, namely, Bolsa de Comercio de Santiago (BCS). The main indicator here is IPSA, whose values are reported ev- ery minute. We choose for this study the year 2010 because on February Abstracts: Oral Communications 29
10, 2010 a huge earthquake of magnitude 8.8 in the Richter scale, the sixth largest earthquake ever recorded by human instruments, followed by a large tsunami, shook most of Chilean territory and flooded several cities at the sea shore. Hundreds of lives were lost and the impact in the economy was large. How was this detected by the BCS? Our results include the report on the daily closing values of IPSA, daily values for mutability, diversity and profitability, possible correlations among these variables, average tendencies of mutability along the hours of the day (not all hours are the same), dependence on foreign stock markets, dy- namic behavior of mutability for different time windows, definition of a new indicator (sensitivity ) capable of anticipating large changes in the stock markets and possible criteria to tune sensitivity as a tool for stock market operations. [1] E. E. Vogel, G. Saravia, L. V. Cortez, Physica A 391, 1591-1601 (2012) (doi:10.1016/j.physa.2011.09.005). †Email address: [email protected].
A non-phenomenological model to explain population growth behaviors
Fabiano Lemes Ribeiro Universidade Federal de Lavras (UFLA) – Minas Gerais – Brazil
Will be proposed a non-phenomenological model for population growth based on the interaction between the individuals which compose the sys- tem. Will be considered that the individuals interacting by cooperation and competition. As consequence of this interaction will be showed that some well-known phenomenological population growth (as Malthus, Ver- hulst, Gompertz, Richards, Von Foerster, and power-law growth models) are reached as particular cases. Moreover other ecological behaviors can be seem as an emergent behavior of such interaction. For instance the Allee effect, which is the characteristic of some population to increase the population growth rate at small population size. While the models presented in the literature explain the Allee effect by phenomenologi- cal ideas, the model that will be presented explain such effect by the own interaction between the individuals. The model will be confronted Abstracts: Oral Communications 30 with empirical data in order to justify its formulation. Other interesting macroscopic emergent behavior from the model proposed is the observa- tion of a regime of population divergence at finite time. It is interest- ing that such characteristic is observed in the human global population growth. Will be shown that in regime of cooperation, the model fit very well to the human population growth data since year 1000 A.D. up to the nowadays.
Universality of Tsallis non-extensive statistics and time series analysis: Theory and applications Georgios P. Pavlos1 & L. P. Karakatsanis1 & A. C. Iliopoulos1 & M. N. Xenakis2 & E. G. Pavlos3 1Department of Electrical and Computer Engineering, Democritus University of Thrace (DUTH) – Xanthi – Greece 2German Research School for Simulation Sciences (GRS-SIM) – Aachen – Germany 3Department of Physics, Aristotle University of Thessaloniki (AUTH) – Thessaloniki – Greece Near thermodynamic equilibrium statistics and dynamics are two sepa- rated but fundamental elements of the physical theory. Also, at thermo- dynamical equilibrium, nature reveals itself as a Gaussian and macroscop- ically uncorrelated process simultaneously with unavoidable or inevitable and objective deterministic character. However, modern evolution of the scientific knowledge reveals the equilibrium characteristics of the physi- cal theory as an approximation or the limit of a more synthetic physical theory which is characterized as complexity. The new physical charac- teristics of complexity theory can be manifested as a physical system is driven in far from equilibrium states. Generally, the traditional scientific point of view is the priority of dynamics over statistics. That is dynamics creates statistics. However for a complex system the holistic behaviour does not permit easily such a simplification or division of dynamics and statistics. From this point of view Tsallis statistics and fractal or strange kinetics are two faces of the same complex and holistic (non-reductionist) reality. As Tsallis statistics is an extension of Boltzmann-Gibbs statis- tics, we can support that the thermal and the dynamical character of a Abstracts: Oral Communications 31 complex system are the manifestation of the same physical process which creates extremized thermal states (extremization of Tsallis entropy), as well as dynamically ordered states. From this point of view the Feyn- man path integral formulation of the statistical physical theory and of the quantum probabilistic theory indicates the indivisible thermal and dynamical character of physical reality. After Heisenberg’s revolution- ary subst itution of physical magnitudes by operators and the follow- ing probabilistic interpretation of Heisenberg operationalistic concepts and Schrodinger wave functions done by Max Born, probability obtained clearly a new realistic and ontological character concerning the founda- tion of physics. Moreover, the development of complexity theory caused the extension of the probabilistic character of dynamics from microscopic (quantum theory) to macroscopic (classical theory) level of reality. This showed the deeper meaning of the Boltzmann entropy principle through the fractal extension of dynamics, as well as the q-extension of statistics according to Tsallis non-extensive entropy theory. Modern evolution of physical theory, as it was described previously, is highlighted in Tsallis q-generalization of the Boltzmann-Gibbs (B-G) statistics which includes the classical (Gaussian) statistics, as the q = 1 limit of thermodynamical equilibrium. Far from equilibrium, the statistics of the dynamics follows the q-Gaussian generalization of the B-G statistics or other more gen- eralized statistics. At the same time, Tsallis q-extension of statistics is related to the fractal generalization of dynamics. However, for complex systems, their holistic behaviour does not easily permit such a simpli- fication and division of dynamics and statistics. The Tsallis extension of statistics and the fractal extension of dynamics as strange kinetics are two faces of the same complex and holistic (non-reductionist) reality. Moreover, the Tsallis statistical theory including the Tsallis extension of entropy to what is known as q-entropy principle and the fractal general- ization of dynamics parallely to the scale extension of relativity theory, are the cornerstones of modern physical theory related to non-linearity and non-integrability as well as to the non-equilibrium ordering and the self-organization principle of nature. The theoretical concepts underly- ing Tsallis statistical theory and fractal dynamics can be used for the study of experimental time series extracted by complex systems obser- vations. For this we apply concerning theoretical concepts of Tsallis non-equilibrium statistical mechanics to analyze and predict statistical Abstracts: Oral Communications 32 and dynamical parameters of signals corresponding to novel algorithms concerning theoretical concepts of non-equilibrium dynamics to analyse signals corresponding to: a) cosmic stars and cosmic rays, b) space plas- mas dynamics such as magnetospheric and solar systems, c) atmospheric dynamics and klima, d) earthquake dynamics and e) cardiac and brain dynamics.
Towards a large deviation theory for statistical-mechanical complex systems
Guiomar Ruiz Lopez1 & Constantino Tsallis2 1Universidad Politecnica de Madrid (UPM) – Madrid – Spain 2Centro Brasileiro de Pesquisas F´ısicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil
The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on W the additive entropy SBG = kB i=1 pi ln pi. Its optimization under − βEi appropriate constraints yields the celebrated BG weight e− . An ele- mentary large-deviation connectionP is provided by N independent binary variables, which, in the N limit yields a Gaussian distribution. The probability of having n→= N/ ∞ 2 out of N throws is governed by the Nr 6 exponential decay e− , where the rate function r is directly related to the relative BG entropy. To deal with a wide class of complex systems, nonextensive statistical mechanics has been proposed, based on the non- W q 1 P =1 p − i i additive entropy Sq = kB q 1 (q ; S1 = SBG). Its optimization − ∈ R βqEi z 1/(1 q) z z yields the generalized weight eq− (eq [1+(1 q)z] − ; e1 = e ). We numerically study large deviations≡ for a strongly− correlated model which depends on the indices Q [1, 2) and γ (0, 1). This model pro- vides, in the N limit ( γ),∈Q-Gaussian distributions,∈ ubiquitously observed in nature→ ∞ (Q 1∀ recovers the independent binary model). → Nrq We show that its corresponding large deviations are governed by eq− 1/(q 1) Q 1 ( 1/N − if q > 1) where q = γ(3−Q) +1 1. This q-generalized illustration∝ opens wide the door towards− a desirable≥ large-deviation foun- dation of nonextensive statistical mechanics. Abstracts: Oral Communications 33
Environmental aspects of superstatistics: Temperature
G. Cigdem Yalcin1 & Christian Beck2 1Department of Physics, Istanbul University – Istanbul – Turkey 2School of Mathematical Sciences, Queen Mary, University of London (QMUL) – London – UK Superstatistical techniques are powerful tools to describe general classes of complex systems. The applicability of these techniques to real-world problems is the prominent property of the superstatistics concept. Some of these numerous interesting applications are turbulence [1–4], defect turbulence [5], share price dynamics [6,7], random matrix theory [8,9] random networks [10], wind velocity fluctuations [11,12], hydro-climatic fluctuations [13], the statistics of train departure delays [14], models of the metastatic cascade in cancerous systems [15] scattering processes in high-energy physics [16] and complex systems of solid state physics [17]. More recently we have shown that superstatistical techniques could be also successfully applied to environmental aspects of surface temperature distributions [18]. In this presentation, we will discuss that superstatisti- cal distributions f(β) are very different at different geographic locations, and typically exhibits a double-peak structure for long- term data. For some of our data sets we also find a systematic drift due to global warm- ing. [1] C. Beck, Phys. Rev. Lett. 87, 180601 (2001); [2] A. Reynolds, Phys. Rev. Lett. 91, 084503 (2003); [3] C. Beck, E. G. D. Cohen, H. L. Swinney, Phys. Rev. E 72, 056133 (2005); [4] C. Beck, Phys. Rev. Lett. 98, 064502 (2007); [5] K. E. Daniels, C. Beck, E. Bodenschatz, Physica D 193, 208 (2004); [6] M. Ausloos, K. Ivanova, Phys. Rev. E 68, 046122 (2003); [7] E. Van der Straeten, C. Beck, Phys. Rev. E 80, 036108 (2009); [8] A. Y. Abul-Magd, Physica A 361, 41 (2006); [9] A. Y. Abul-Magd, B. Dietz, T. Friedrich, A. Richer, Phys. Rev. E 77, 046202 (2008); [10] S. Abe, S. Thurner, Phys. Rev. E 72, 036102 (2005); [11] S. Rizzo, A. Rapisarda, AIP Conf. Proc. 742, 176 (2004); Abstracts: Oral Communications 34
[12] T. Laubrich, F. Ghasemi, J. Peinke, H. Kantz, arXiv:0811.3337; [13] A. Porporato, G. Vico, P. A. Fay, Geophys. Res. Lett. 33, L15402 (2006); [14] K. Briggs, C. Beck, Physica A 378, 498 (2007); [15] L. Leon Chen, C. Beck, Physica A 387, 3162 (2008); [16] C. Beck, Eur. Phys. J. A 40, 267 (2009); [17] G. C. Yalcin, C. Beck, Phys. Lett. A 376, 2344 (2012); [18] G. C. Yalcin, C. Beck, Physica A 392, 21, 5431 (2013).
Fluids in curved space
Hans Herrmann Computational Physics for Engineering Materials Group, Institut fur¨ Baustoffe (IfB), Eidgen¨ossische Technische Hochschule Zurich¨ (ETH Zurich)¨ – Zurich¨ – Switzerland Departamento de F´ısica, Universidade Federal do Cear´a(UFC) – Cear´a– Brazil By inserting the spatial metric into the equations of motion of a fluid and using contravariant coordinates it becomes possible to obtain the velocity field of the flow in an arbitrarily curved geometry by just solv- ing the Lattice Boltzmann equations in Euclidean space on a cubic grid. This allows for instance to obtain Taylor-Couette rolls between concentric cylinders, spheres or tori in a rectangle with a metric tensor describing constant curvature. A “campylotic” medium consisting of randomly dis- tributed curved patches gives a non-monotonic dependence on the density of patches. Also relativistic fluids can be canonically treated by the Lat- tice Boltzmann method by considering two distribution functions and identifying the physical and the numerical maximal velocities. This al- lows studying very efficiently shock waves in the quark-gluon plasma and supernova explosions. The ultrarelativistic limit can be achieved by de- veloping the Juttner¨ distribution in polynomials. Also a treatment of the q-generalization of the relativistic Navier-Stokes equation becomes feasible in this way. Abstracts: Oral Communications 35
Restricted random walk model as a new testing ground for the applicability of q-statistics
⋆, Henrik Jeldtoft Jensen † Complexity & Networks Group and Department of Mathematics, Imperial College London – London – UK We present exact results obtained from Master Equations for the prob- T ability function P (y,T ) of sums y = t=1 xt of the positions xt of a discrete random walker restricted to the set of integers between L and L. We study the asymptotic propertiesP for large values of L and−T . For a set of position dependent transition probabilities the functional form of P (y,T ) is with very high precision represented by q-Gaussians when 2 T assumes a certain value T ∗ L . The domain of y values for which the q-Gaussian apply diverges with∝ L. The fit to a q-Gaussian remains of very high quality even when the exponent a of the transition probability g(x) = x/L a + p with 0 < p 1 is different from 1, although weak, but essential,| | deviation from the≪q-Gaussian does occur for a = 1. To 6 assess the role of correlations we compare the T dependence of P (y,T ) for the restricted random walker case with the equivalent dependence for a sum y of uncorrelated variables x each distributed according to 1/g(x). Reference: U. Tirnakli, H. J. Jensen, C. Tsallis, Restricted random walk model as a new testing ground for the applicability of q-statistics, EPL 96, 40008 (2011). arXiv:1105.6184. ⋆Collaborative work together with: Ugur Tirnakli and Constantino Tsal- lis. †Email address: [email protected]. Abstracts: Oral Communications 36
Combinatorial basis for Tsallis entropy and its applications
Hiroki Suyari Graduate School of Advanced Integration Science, Chiba University – Chiba – Japan The combinatorial basis for Tsallis entropy is presented along the line of Boltzmann’s original approach, starting from the fundamental nonlinear differential equation dy/dx = yq. The most general combinatorial expres- sion for Tsallis entropy recovers the four typical structures: (i) additive duality “q 2 q”; (ii) multiplicative duality “q 1/q”; (iii) q-triplet; (iv) multifractal↔ − triplet. In the presentation, new result↔ s associated with the combinatorial basis are also presented. [1] C. Tsallis, What should a statistical mechanics satisfy to reflect nature?, Physica D 193, 3–34 (2004); [2] L. Nivanen, A. Le Mehaute, Q. A. Wang, Generalized algebra within a nonextensive statistics, Rep. Math. Phys. 52, 437-444 (2003); [3] E. P. Borges, A possible deformed algebra and calculus inspired in nonex- tensive thermostatistics, Physica A 340, 95–101 (2004); [4] H. Suyari, Generalization of Shannon-Khinchin axioms to nonextensive sys- tems and the uniqueness theorem for the nonextensive entropy, IEEE Trans. Inform. Theory 50, 1783–1787 (2004); [5] H. Suyari, M. Tsukada, Law of Error in Tsallis Statistics, IEEE Trans. Inform. Theory 51, 753–757 (2005); [6] H. Suyari, Mathematical structure derived from the q-multinomial coeffi- cient in Tsallis statistics, Physica A 368, 63–82 (2006); [7] H. Suyari, T. Wada, Multiplicative duality, q-triplet and (µ,ν,q)-relation derived from the one-to-one correspondence between the (µ,ν)-multinomial coefficient and Tsallis entropy Sq, Physica A 387, 71–83 (2008). Email address: [email protected]. Abstracts: Oral Communications 37
Statistical mechanics from the point of view of information geometry
Jan Naudts Physics Department, University of Antwerp – Wilrijk-Antwerpen – Belgium
The Boltzmann-Gibbs distribution is an exponential family of probabil- ity distributions. As a consequence it has a dual Legendre structure. The latter is well-known to physicists as the duality between energy and entropy. The exponential family forms a differentiable manifold which is the object of study in information geometry [1]. The natural metric is that of Fisher. It can be obtained from the matrix of second derivatives of the relative entropy. The traditional approach to non-extensive statistical mechanics starts from the maximum entropy principle. In our alternative approach [2–5] the notion of a deformed exponential family is the central concept. A characteristic property of an exponential family is that the Fisher infor- mation matrix is constant along fibers of minimal relative entropy [6]. In non-extensive statistical mechanics two types of relative entropies are in use [6,7]. In the mathematics literature they are called diver- gences of the Csisz´ar type and of the Bregman type, respectively. We use our characterization to argue that the Bregman type relative entropy is preferable in the context of the Tsallis distribution [6]. [1] S. Amari, H. Nagaoka, Methods of information geometry (American Math- ematical Society & Oxford University Press, 2000); [2] J. Naudts, J. Ineq. Pure Appl. Math. 5, 102 (2004); [3] J. Naudts, Entropy 10, 131–149 (2008); [4] J. Naudts, B. Anthonis, Mod. Phys. Lett. B 26, 1250062 (2012); [5] J. Naudts, B. Anthonis, The exponential family in abstract information the- ory, GSI 2013 LNCS proceedings, F. Nielsen, F. Barbaresco eds., (Springer, 2013), p. 265–272; [6] C. Tsallis, Introduction to nonextensive statistical mechanics (Springer Ver- lag, 2009); [7] J. Naudts, Rev. Math. Phys. 16, 809–822 (2004), 21, 947–948 (2009). Email address: [email protected]. Abstracts: Oral Communications 38
Tsallis’ entropy for central potentials: Improved bounds and uncertainty relations Jes´us S´anchez-Dehesa University of Granada (UGR) – Granada – Spain Further properties of inequality type for the Tsallis entropy of D-dimen- sional physical systems associated with their position and momentum probability distributions are encountered in terms of various density- functional-based observables which are described by power-like positon and momentum expectation values. Then, the results are used to find uncertainty relations, which are later compared with the elegant general expressions of Rajagopal and Maassen-Uffink. Later, the improvement of corresponding uncertainty relation is shown and discussed for systems with spherically-symmetric potentials in terms of the quantum numbers of the physical states and the dimensionality of the system. Applica- tions to some prototypic and real specific quantum systems (Rydberg atoms, oscillator-like systems, ?) will be given. Finally, if time allows it, a large class of D-dimensional central potentials will also be shown to have ground states of the q-Gaussian form, either in position space or in momentum space.
Optimal synchronizability of bearings Jos´eSoares de Andrade Jr. Universidade Federal do Cear´a(UFC) – Cear´a– Brazil Bearings are mechanical dissipative systems that, when perturbed, relax toward a synchronized (bearing) state. Here we find that bearings can be perceived as physical realizations of complex networks of oscillators with asymmetrically weighted couplings. Accordingly, these networks can ex- hibit optimal synchronization properties through fine tuning of the local interaction strength as a function of node degree. We show that, in analogy, the synchronizability of bearings can be maximized by counter- balancing the number of contacts and the inertia of their constituting Abstracts: Oral Communications 39 rotor disks through the mass-radius relation, m rα, with an optimal exponent α = α which converges to unity for∼ a large number of ro- × tors. Under this condition, and regardless of the presence of a long-tailed distribution of disk radii composing the mechanical system, the average participation per disk is maximized and the energy dissipation rate is homogeneously distributed among elementary rotors.
Information fusion and metrics using coupled states Kenric P. Nelson Raytheon Company – California – USA The methods of nonextensive statistical mechanics and information ge- ometry are interpreted to define a nonlinear coupling between statistical states. The weighted coupled-product of probabilities is used as both a method for information fusion and shown to be equivalent to the nor- malized Tsallis entropy. Numerical experiments demonstrate that one coupling parameter can replace tens of thousands of linear correlation parameters in fusing the inferences from individual image pixels. Per- formance comparisons with a full covariance matrix and the na¨ıve bayes utilize a risk profile which shows the spectrum of the generalized mean for the true class probabilities. This probability-based performance metric is a transformation of the generalized entropy measure.
Earth’s climate complexity L. P. Karakatsanis1 & G. P. Pavlos1 & A. A. Tsonis2 & A. C. Iliopoulos1 & M. N. Xenakis3 & E. G. Pavlos4 1Department of Electrical and Computer Engineering, Democritus University of Thrace (DUTH) – Xanthi – Greece 2Department of Mathematical Sciences, University of Wisconsin-Milwaukee (UWM) – Wisconsin – USA 3German Research School for Simulation Sciences (GRS-SIM) – Aachen – Germany 3Department of Physics, Aristotle University of Thessaloniki (AUTH) – Thessaloniki – Greece Abstracts: Oral Communications 40
In this study we apply the Tsallis theory as concerns the estimation of q-triplet for the geopotential height (GH) time-series, by analyzing tem- poral and spatial components of the global distribution of month average values, during the period (1948-2012), reveal the presence of strong non- extensive character for both spatial and temporal components. Also no- ticeable differences of the q-triplet estimated at distinct local or temporal regions where found. Moreover theoretical interpretation of our results are presented. The results indicate the existence of spatiotemporal long range correlations and fractal dynamics underlying to the GH signal. This can be understood as a fractal Fokker-Plank process correspond- ing to far from thermodynamic equilibrium stochastic process including anomalous diffusion (non-Gaussian diffusion) character. This is in con- trast to the near equilibrium Gaussian stochastic process. Especially, we summarize the estimation per decade of q-triplet. It is noticeable the complementary character of the q-triplet values between the north and south hemisphere, while the values of the q-triplet for the global planet correspond approximate for the mean value, especially for the q-stat and q-rel values. Also during the first three decades we can observe simul- taneously degrease at the south hemisphere and increase at the north hemisphere of the q-stat values. The global q-triplet presents clearly degreasing profile, especially after 1970. We can support that the de- greasing of the q-stat value especially after 1970 indicates the tendency of the homogenization of the dynamics (approach to Gaussian profile) loss of complexity and long range correlations.
Wavelet coherency in complex systems Liacir dos Santos Lucena Universidade Federal do Rio Grande do Norte (UFRN) – Rio Grande do Norte – Brazil National Institute of Science and Technology of Complex Systems (INCT-SC) – Rio de Janeiro – Brazil When we analyze complex networks and other complex systems it is im- portant to know if two elements or sub-systems are linked or strongly correlated. In other words we need to investigate if they are part of the same group or cluster. If we don’t have this information a priori, we Abstracts: Oral Communications 41 try to infer it from cross correlations between time series (or data series) measured in these sub-systems. Although the standard statistical cross correlation methods may fail in giving an unambiguous result because of their global nature and possible fortuitous coincidences, there are cross- correlation quantities defined in wavelet space that provide a high degree of confidence for evaluating the similarity between the two parts. They are able to quantify the degree of cross-correlation in every scale (time- frequency or distance-wavelenght data intervals). They act as coherence tools capable to identify regions with identical properties, corresponding to the situations in which high cross-correlations are observed simulta- neously in all scales. We have applied this approach to study physical quantities registered in well logs, searching for the continuity and ex- tension of geological structures and trying to find connections between petroleum reservoirs.
The general preferential attachment growth model and nonextensive statistical mechanics
Samura´ıG. Aguiar1 & C. Tsallis2,3 & Luciano R. da Silva1,3 1Universidade Federal do Rio Grande do Norte (UFRN) – Rio Grande do Norte – Brazil 2Centro Brasileiro de Pesquisas F´ısicas (CBPF) – Rio de Janeiro – Brazil 3National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil
In this work we revisit the model of Soares et al (2005) [1] in which they take into account Euclidean distances in between sites of a Network in- stead of topologic distances as in the Barabasi-Albert traditional model. Then numerically it is determined that the probability distribution of a site to have k links is asymptotically given by P (k) proportional to 1/(1 q) expq( k/κ), where expq(x) = [1+(1 q)x] − is the function natu- rally emerging− within nonextensive statistical− mechanics. In the work of Soares et al they established a connection in between the area of Net- works and the Tsallis nonextensive statistical mechanics approach. The previous work is done for d = 2 and here we revisit the model including d = 1 and d = 3 dimensions. Abstracts: Oral Communications 42
[1] D. J. B. Soares, C. Tsallis, A. M. Mariz, L. R. da Silva, Preferential At- tachment Growth Model and Noextensive Statistical Mechanics, Europhysics Letters 70, 70 (2005).
Are there dissipative structures in UEFA competition team ranking?
Marcel Ausloos† Universit´ede Li`ege (ULg) – Li`ege – Belgium Measures of primacy in ranking are presented with application to the 445 soccer teams, as ranked by UEFA. The analysis is based on consid- erations about complex systems, i.e. searching whether power law fits are appropriate to describe some internal non-linear dynamics. It can be so observed that major classes emerge, - surprisingly two in this UEFA case. Whence it seems of interest to raise the question whether a ranking method, like that of UEFA, implicitly induces some inner structure in the ranking distribution. In so doing, several subclasses can be found in particular when the notion of primacy index, as imagined by Sheppard is envisaged. To better perform, several additional indices are discussed, like those of Vitanov. (N.B. These measures can be used to sort out peer classes in more general terms.) Numerical illustrations, through the so called “length ratio”, are illuminating, suggesting dissipative structures implication, as introduced by Nicolis and Prigogine. Thus a hierachical (open space) model, yet with boundary constraints, is suggested. A note on “soccer country ranking” is introduced for further discussion. Con- nection to Tsallis q-entropy is searched for. †Previously at GRAPES, ULG, Li`ege, Belgium, now at R´es. Beauvallon, rue de la Belle Jardiniere, 483/0021 B-4031, Li`ege Angleur, Wallonia-Brussels Federation, still in Belgium, Euroland. Email address: [email protected]. Abstracts: Oral Communications 43
Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil
Newton J. Moura Jr1 & Marcelo B. Ribeiro2 1Instituto Brasileiro de Geografia e Estat´ıstica (IBGE) – Rio de Janeiro – Brazil 2Instituto de F´ısica, Universidade Federal do Rio de Janeiro (UFRJ) – Rio de Janeiro – Brazil This paper discusses the empirical validity of Goodwin’s (1967) macroe- conomic model of growth with cycles by assuming that the individual in- come distribution of the Brazilian society is described by the Gompertz- Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the popula- tion ( 99%), with the Pareto power law, representing the tiny richest part (∼ 1%). In line with Goodwin’s original model, we identify the Gompertzian∼ part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD pa- rameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems. Reference: Physica A 392, 2088-2103 (2013) (arXiv:1301.1090). Abstracts: Oral Communications 44
Enhancement flow in nanoconfined water
1,2, 3,⋆ 4, Jos´eRafael Bordin † & Jos´eS. Andrade Jr. & Alexandre Diehl ‡ & Marcia C. Barbosa1,⊲ 1Instituto de F´ısica, Universidade Federal do Rio Grande do Sul (UFRGS) – Rio Grande do Sul – Brazil 2Institut fur¨ Computerphysik, Universit¨at Stuttgart – Stuttgart – Germany 3Departamento de F´ısica, Universidade Federal do Cear´a(UFC) – Cear´a– Brazil 4Departamento de F´ısica, Instituto de F´ısica e Matem´atica, Universidade Federal de Pelotas (UFPEL) – Rio Grande do Sul – Brazil We investigate through non-equilibrium molecular dynamic simulations the flow of core-softened fluids inside nanotubes. Our results reveal a anomalous increase of the overall mass flux for nanotubes with suffi- ciently smaller radii. This is explained in terms of a transition from a single-file type of flow to the movement of an ordered-like fluid as the nanotube radius increases. The occurrence of a global minimum in the mass flux at this transition reflects the competition between the two characteristics length scales of the core-softened potential. Moreover, by increasing further the radius, another substantial change in the flow be- havior, which becomes more evident at low temperatures, leads to a local minimum in the overall mass flux. Microscopically, this second transition results from the formation of a double-layer of flowing particles in the con- fined nanotube space. These special nano-fluidic features of core-softened particles closely resemble the enhanced flow behavior observed for liquid water inside carbon nanotubes. Email addresses: †[email protected], ⋆ ⊲ [email protected], ‡[email protected], marcia.barbosa@ufrgs- .br.
Tsallis entropy composition: a geometric view Nikos Kalogeropoulos Weill Cornell Medical College in Qatar (WCMC-Q) – Doha – Qatar. Probably the biggest formal difference between the Tsallis and the BGS entropies, lies in their composition properties, as it can be seen through Abstracts: Oral Communications 45 a comparison of their axiomatic formulations. We explore aspects of the Tsallis entropy composition. We take a geometric viewpoint in our treatment. In addition to the differential, we also stress the synthetic approach as the latter may be of some use in quantum gravity.
Distinguishing noise from chaos: an Information Theory approach
O. A. Rosso1,2 & L. C. Carpi3 & M. T. Mart´ın4 & H. A. Larrondo 5 & F. Olivares 5 & L. Zunino 6 & M. G´omez Ravetti 7 & A. Plastino 4 1Instituto de F´ısica, Universidade Federal de Alagoas (UFAL) – Alagoas – Brazil 2Laboratorio de Sistemas Complejos, Facultad de Ingenier´ıa, Universidad de Buenos Aires (UBA) – Ciudad Aut´onoma de Buenos Aires – Argentina 3LaCCAN/CPMAT - Instituto de Computa¸c˜ao, Universidade Federal de Alagoas (UFAL) – Alagoas – Brazil 4Instituto de F´ısica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP) – La Plata – Argentina 5Facultad de Ingenier´ıa, Universidad Nacional de Mar del Plata (UNMdeP) – Mar del Plata – Argentina 6Centro de Investigaciones Opticas (CIOp), Universidad Nacional de La Plata (UNLP) – La Plata – Argentina 7Departamento de Engenharia de Produ¸c˜ao, Universidade Federal de Minas Gerais (UFMG) – Belo Horizonte – Brazil Deterministic chaotic systems share with truly stochastic processes sev- eral properties that make them almost undistinguishable. In this commu- nication we introduce a two representation space in which, its horizontal and vertical axis are suitable functionals of the pertinent probability dis- tribution. These planes, to be called: a) causality statistical complexity - entropy plane, and b) causality Fisher information - Shannon entropy plane, H×C; allow to quantifies the global-global and global- local characteristicH × of F the corresponding associated probability distribu- tion to the time series generated by the dynamical process under study. These three functionals (normalized Shannon entropy, ; Fisher infor- H mation measure, ; and statistical complexity ) are evaluated using the Bandt and PompeF permutation recipe to assignC a probability distribution function to the time series generated by the system. Several stochastic Abstracts: Oral Communications 46
k (noises with f − , k 0, power spectrum, fBm and fGn) and chaotic pro- cesses (27 chaotic maps)≥ are analyzed so as to illustrate the approach. The main achievement of this communication is the system’s localization in a causal entropy-complexity plane and causal Shannon-Fisher plane displays typical specific features associated with its dynamics’ nature, allowing a clearly distinguishing between stochastic and nonlinear low dimensional chaotic dynamics in our two representation spaces, some- thing that is rather difficult otherwise. Additive noise contamination k (noises with f − , k 0, power spectrum) of chaotic time series planar localization effects are≥ also reported.
Phenomenological and theoretical reconstruction in the framework of information geometry science is the process of reconstructing theory from data Paul Bourgine Ecole´ Polytechnique & Centre National de la Recherche Scientifique (CNRS) – Paris – France Complex systems must be observed in vivo, providing multilevel data collection protocols. And they require formalisms to reconstruct their intra-level and inter-level dynamics, and their capacity to adapt to per- turbations from their changing environments. A first way to think a required formalism for reconstructing the multi-level dynamics of a com- plex systems is through assimilation of multi-level data by a nonpara- metric model as done by the brain. This way leads to phenomenological reconstructions and measurement of quality of phenomenological recon- struction of the data can be done inside the information geometry frame- work. The most elegant way is to require formalisms that provide the littlest possible formulation of the integrated model of the multi-level stochastic dynamics of a complex system. This way leads to theoretical reconstructions and measurement of quality of theoretical reconstruction can again be done inside the information geometry framework. If we consider the shortest model for a given quality, the size of the best model will increase with the quality. But for better understanding of a class of complex systems, shorter models can be required to capture the most im- portant qualitative and theoretical features. And two common ones are Abstracts: Oral Communications 47 long term memory and path dependency as well as adaptation to their environmental constraints at the border of chaos. Long term memory will be exemplified through the projection theorem in statistical physics and its link with information theory. The border of chaos will be ex- emplified through the class of systems having a strong capacity to treat information.
Generalized entropic measures of quantum correlations
Ra´ul Rossignoli & N. Canosa & L. Ciliberti Departamento de F´ısica-IFLP, Universidad Nacional de La Plata (UNLP) – La Plata – Argentina
We discuss a general measure of nonclassical correlations for bipartite quantum systems, based on general concave entropic forms [1]. Defined as the minimum information loss due to a local measurement in one of the systems, in the case of pure states it reduces to the generalized entangle- ment entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be nonzero in non-entangled (separa- ble) states, vanishing just for classically correlated states with respect to the measured system, like the quantum discord. For the von Neumann entropy, the present measure becomes the so-called one-way information deficit, whereas for the q = 2 Tsallis entropy, it reduces to the geomet- ric discord. The general stationary condition for the minimizing local measurement is also provided. Moreover, closed analytic expressions for this quantity, valid for general states of two-qubit systems, are derived for the q = 2 and q = 3 Tsallis entropies. As appli cation, we analyze the case of states with maximally mixed marginals, where a general eval- uation is provided, as well as X states and the mixture of two aligned states. Comparison with the corresponding entanglement monotones is also shown. [1] R. Rossignoli, N. Canosa, L. Ciliberti, Phys. Rev. A 82, 052342 (2010); A 84, 052329 (2011); A 86, 022104 (2012). Abstracts: Oral Communications 48 Data analysis of elections
Renio dos Santos Mendes Universidade Estadual de Maring´a(UEM) – Paran´a– Brazil National Institute of Science and Technology of Complex Systems (INCT-SC) – Rio de Janeiro – Brazil Recent results of data analysis of elections are reviewed. More specifically, power law distribution of votes, efforts aiming to model this behavior, dis- tribution of votes when considering the weight of the parties, polarization of the voters, electoral turnout rates, detection of fraud, and allometric behavior of the number of candidates and of member of political parties as function of population of voters are discussed.
Thermodynamical consequences of the effective-temperature concept: heat, work, Carnot cycle, Clausius theorem, and entropy definition
Andr´eM. C. Souza1,4 & Evaldo M. F. Curado2,4 & Fernando D. Nobre2,4 & Roberto F. S. Andrade3,4 1Universidade Federal de Sergipe (UFS) – Sergipe – Brazil 2Centro Brasileiro de Pesquisas F´ısicas (CBPF) – Rio de Janeiro – Brazil 3Universidade Federal da Bahia (UFBA) – Bahia – Brazil 4National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil The concept of effective temperature θ in a pure mechanical model has been discussed within the framework of the non-extensive statistical me- chanics [1]. In such case, it has been proven that this parameter, which is directly related to the density as well as to the interactions among vortices, plays the role of the actual temperature when generalized quan- tities such as entropy, internal energy, free energy, and heat capacity are conveniently and consistently defined. Now we explore further con- sequences of this definition. Particularly, we investigate the properties of an analogous to a Carnot cycle in terms of isothermal and adiabatic paths. They correspond, respectively, to processes where θ = constant and entropy S = constant. By direct evaluation of the heat and work Abstracts: Oral Communications 49 in the process, we show that the efficiency of such cycle is given only in terms of the effective temperatures θ1 and θ2 of the operating heat reservoirs. Next we consider a thermodynamical definition of work and heat transfer, and consider the hypothesis that the analogous Clausius statement to the second law is valid. Under this hypothesis, we prove the Clausius theorem for this system in terms of effective temperature con- cept, which leads to thermodynamical entropy expression. The obtained analytical expression is coincident to that derived within the framework of non-extensive statistical mechanics. [1] Fernando D. Nobre, Andre M. C. Souza, Evaldo M. F. Curado, Effective- temperature concept: A physical application for non-extensive statistical me- chanics, Phys. Rev. E 86, 061113 (2012).
Imaging in complex media: Recent progresses
Roger Maynard Laboratoire de Physique et de Mod´elisation de la Mati`ere Condens´ee, Universit´eJoseph Fourier (UJF) & Centre National de la Recherche Scientifique (CNRS) – Grenoble – France
The Cancho i Ferrer - Sol´emodel does not explain Zipf’s Law
Ronald Dickman Departamento de Fisica, Universidade Federal de Minas Gerais (UFMG) – Minas Gerais – Brazil National Institute of Science and Technology of Complex Systems (INCT-SC) – Rio de Janeiro – Brazil We examine the cost-minimization problem posed by Ferrer i Cancho and Sol´ein their information-theory based communication model [1], proposed in efforts to explain Zipf’s Law (that is, a power-law frequency- rank relation for words in written texts). Using a simple inequality, we obtain the exact minimum-cost solution as a function of the parameter Abstracts: Oral Communications 50
λ, as obtained previously via other methods [2–4] (λ defines the relative weights of speaker’s and listener’s costs). We show that at the phase transition, the minimum-cost solutions do not correspond to a power law except for a vanishingly small subset, even if we impose the additional condition of equal costs to speaker and listener [5]. Finally we consider the model at finite temperature using mean-field theory and entropic Monte Carlo simulation, and find a line of discontinuous phase transitions in the λ-T plane. The simulations yield no evidence for a power-law frequency-rank distribution. [1] R. Ferrer i Cancho, R. V. Sol´e, PNAS 100, 788 (2003); [2] R. Ferrer i Cancho, A. D´ıaz-Guilera, J. Stat. Mech.: Theory Exp. P06009 (2007); [3] A. Trosso, Master’s thesis, 2008, University of Turin, Italy; [4] M. Prokopenko, N. Ay, O. Obst, D. Polani, J. Stat. Mech. P11025 (2010); [5] R. Dickman, N. R. Moloney, E. G. Altmann, J. Stat. Mech. P12022 (2012).
An Information-based tool for inferring the nature of deterministic sources in real data
Rosane Riera & A. S. Ribeiro Departamento de F´ısica, Pontif´ıcia Universidade Cat´olica (PUC-Rio) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil
The scope of the paper is to find signatures of the forces controlling com- plex systems modeled by Langevin equations, by recourse to information- theory quantifiers. We evaluate in detail the permutation entropy (PE) and the permutation statistical complexity (PSC) measures for two sim- ilarity classes of stochastic models, characterized by either drifting or reversion properties, and employ them as a reference basis for the in- spection of real series. New relevant model parameters arise as compared to standard entropy measures. We determine the normalized PE and PSC curves according to them over a range of permutation orders n and infer the limiting measures for arbitrary large order. We found that the PSC measure is strongly scale-dependent, with systems of the drifting class showing crossovers as n increases. This result gives warning signs Abstracts: Oral Communications 51 about the proper interpretation of finite-scale analysis of complexity in general processes. Conversely, a key n-invariant outcome arises, that is, the normalized PE values for both classes of models keep complementary for any n. We argue that both PE and PSC measures enable one to unravel the nature (drifting or restoring) of the deterministic sources un- derlying complexity. We conclude by investigating the presence of local trends in stock price series.
From multiplicity to entropy
Rudolf Hanel & Stefan Thurner Medical University of Vienna (MUV) – Vienna – Austria Shannon and Khinchin built their foundational information theoretic work on four axioms that completely determine the information-theoretic entropy to be of Boltzmann-Gibbs type, SBG = i pi log pi. For non-additive systems the so called separation axiom− (Shannon-Khinchin axiom 4) is not valid. It can be shown that wheneverP this axiom is is replaced by the requirement that entropic forms are of trace-form, S = s(p ), then S takes a more general form, S W Γ(d +1, 1 i i c,d ∝ i − c log pi), where c and d are characteristic scaling exponents. P P As a consequence non-additive systems, i.e. systems where SBG is non-extensive (scales linearly with system size), can possess assymptot- ically extensive generalized trace-form entropies S(c,d). The exponents (c,d) parametrize equivalence classes which precisely characterize all in- teracting and non interacting (statistical) system in the thermodynamic limit [1], comprizing systems typically exhibiting power laws or stretched exponential distributions. However, the generalized extensive entropy is not necessarily identi- cal with the generalized entropy functional required in a maximum en- tropy principle. Both concepts are closely related but distinct from each other. The generalized entropy functional in fact derives directly from Boltzmann entropy, i.e. the multiplicities of states. In particular, while Boltzmann entropy takes the form of the Shannon entropy for indepen- dent or weakly correlated systems, Boltzmann entropy can take different functional forms for strongly correlated systems. Whether a system is Abstracts: Oral Communications 52 weakly or strongly correlated depends on whether or not a system breaks a certain invariance property. We show that the entropy and the constraints a systems requires are determined by the multiplicity structure of phase-space. In particular it is the first Shannon-Khinchin Axiom that allows to properly distinguish between entropy and constraints. Systems that require generalized en- tropies have phase-spaces growing non-exponentially with system size. This is relevant e.g. for aging systems and non-Markovian systems with long-term memory, as e.g. random walks [2,3] where agents cross over from making random choices to making persistent choices over time de- pending on the history of the agent (or other forms of self-reinforcing Dirichlet-processes). Also self-organized critical systems such as sand piles or particular types for spin systems with densifying interactions may be found in this classes of strongly correlated sytems. In this contribution we largely follow the lines of thought presented in [1–3] and recent work together with Murray Gell-Mann, soon to be published. [1] R. Hanel, S. Thurner, A comprehensive classification of complex statistical systems and an axiomatic derivation of their entropy and distribution func- tions, Europhys Lett. 93, 20006 (2011); [2] R. Hanel, S. Thurner, When do generalized entropies apply? How phase space volume determines entropy, Europhys Lett 96, 50003 (2011); [3] S. Thurner, R. Hanel, What do generalized entropies look like? An ax- iomatic approach for complex, non-ergodic systems, in Recent advances in Generaliized Information Measures and Statistics, Bentham Science eBook, (in production 2013).
Some properties of memory retrieval in an associative memory neural network for conscious and unconscious mental behavior Roseli S. Wedemann1 & Maheen F. Siddiqui2 & Henrik J. Jensen2 1Institute of Mathematics and Statistics, State University of Rio de Janeiro (UERJ) – Rio de Janeiro – Brazil 2Department of Mathematics, Imperial College London – London – United Kingdom Abstracts: Oral Communications 53
We study properties of the topologies and dynamics of neuronal systems, to understand brain and mental processes, based on connexionist mod- els [1–6]. It is possible to study how global emergent behavior arises from the interactions among neurons of the parallel processing neuronal networks, with computer simulations. We will present a neural network model, whereby some interplay of conscious and unconscious activities may be described by associative memory mechanisms [3]. In our model, memory retrieval can be achieved through simulated an- nealing, which is a phase space sampling technique. We analyse the behavior of the network under different assumptions on the way simu- lated annealing is performed on the model [7,8]. We will show some properties of the dynamics of memory access, obtained from measure- ments of quantities such as frequencies of access of memory traces and avalanche sizes in computer simulations. We found that when general- ized statistical mechanics is used in the annealing procedure, instead of the Boltzmann machine, there is a power-law behavior for the avalanche size distribution, which is similar to fMRI data of cluster activation in the brain [9]. Knowledge from areas such as neurophysiology, psychiatry, psychology, computer science, mathematics and statistical mechanics can be com- bined, so we can better understand mechanisms which underlie brain and mental processes [1–9]. This knowledge may contribute to the un- derstanding of therapeutic procedures and to the development of models of artificial machines and cognitive devices [1]. [1] J. G. Taylor, A Review of Models of Consciousness. In: V. Cutsuridis, A. Hussain, J. G. Taylor (eds.), Perception-Action Cycle Models, Architectures, and Hardware (Springer Series in Cognitive and Neural Systems, vol. 1, 335- 357, 2011); [2] L. A. V. Carvalho, D. Q. Mendes, R. S. Wedemann, Creativity and Delu- sions: The Dopaminergic Modulation of Cortical Maps, Lecture Notes in Com- puter Science 2657, 511-520 (2003); [3] R. S. Wedemann, R. Donangelo, L. A. V. Carvalho, Generalized Memory Associativity in a Network Model for the Neuroses, Chaos 19, 015116-(1-11) (2009); [4] S. Freud, Remembering, Repeating and Working-Through (Standard Edi- tion, Vol. XII. The Hogarth Press, London, (1953-74). First German edition, 1914); Abstracts: Oral Communications 54
[5] E. Kandel, Psychiatry, Psychoanalysis, and the New Biology of Mind (American Psychiatric Publishing, Inc., Washington D.C., 2005); [6] J. Shedler, The Efficacy of Psychodynamic Psychotherapy, American Psy- chologist 65(2), 98-109 (2010); [7] W. C. Barbosa, Massively Parallel Models of Computation (Ellis Horwood Limited, England, 1993); [8] C. Tsallis, D. A. Stariolo, Generalized Simulated Annealing, Physica A 233, 395–406 (1996); [9] E. Tagliazucchi, P. Balenzuela, D. Fraiman, D. R. Chialvo, Criticality in large-scale brain fMRI dynamics unveiled by a novel point process analysis, Frontiers in Physiology Fractal Physiology 3, Article 15 (2012). |
Beyond the triangle – Brownian motion, Itˆo stochastic calculus, and Fokker-Planck equation: fractional generalizations Sabir Umarov University of New Haven (UNH) – Connecticut – United States One of Albert Einstein’s Annus Mirabilis 1905 papers, titled “Uber¨ die von der molekularkinetischen Theorie der W¨arme geforderte Bewegung von in ruhenden Flussigkeiten¨ suspendierten Teilchen” (“On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat”), was devoted to the theoretical explanation of Brownian motion. A little earlier (in 1900) Bachelier pub- lished his doctoral dissertation “Th´eorie de la sp´eculation” (“The Theory of Speculation”) modeling Brownian motion from the economics point of view. In 1908 Langevin published his work with a stochastic differential equation which was “understood mathematically” only after a stochastic calculus was introduced by Itˆoin 1944-48. The Fokker-Planck equation, a deterministic form of describing the dynamics of a random process in terms of transition probabilities, was invented in 1913-17. Its com- plete “mathematical understanding” become available after the appear- ance of the distribution (generalized function) theory (Sobolev (1938), Schwartz (1951)) and was embodied in Kolmogorov’s backward and for- ward equations. Today the triple relationship between Brownian motion, Abstracts: Oral Communications 55
Itˆostochastic differential equations driven by Brownian motion and their associated Fokker-Planck-Kolmogorov (FPK) partial differential equa- tions is well known. The talk will be devoted to fractional generalizations of this triple relationship between the driving process, corresponding SDEs, and associated deterministic fractional order pseudo-differential equations. In the last few decades, fractional FPK type equations have been used in modeling various complex processes in physics, finance, hy- drology, cell biology, etc. Complexity includes phenomena such as weak or strong correlations, different sub- or super-diffusive modes, memory and jump effects. For example, experimental studies of the motion of proteins or other macromolecules in a cell membrane show apparent sub- diffusive motion with several simultaneous diffusive modes. The driving process of a stochastic differential equation plays a key role in the dynam- ics and evolution of the solution to that SDE. The processes associated with fractional order FPK equations are usually driven by complex pro- cesses. Even in the simplest case of the fractional equation ∂βu = ∆u, where ∆ is the Laplace operator, and ∂β is a fractional derivative of order 0 <β< 1, the driving process is not even a L´evy process. We will briefly discuss that the driving processes related to fractional FPK equations are limit processes of continuous time random walks (CTRW).
Interplay between forest fire distribution and forest age structure
S´ergio Galv˜ao Coutinho Universidade Federal de Pernambuco (UFPE) – Pernambuco – Brazil We investigate via a cellular automata model the interplay between the distribution of long-term and large-scale forest fires and the forest age distribution. Particularly, we associate the age of the trees (or acres of forest) with the local heterogeneity existing in forested environments to determine their degree of flammability. Abstracts: Oral Communications 56
Mean-field theories and quasi-stationary simulations of epidemics models on complex networks A. S. Mata & S´ılvio C. Ferreira Departamento de F´ısica, Universidade Federal de Vi¸cosa (UFV) – Minas Gerais – Brazil In this communication, we will present a quenched mean-field (QMF) theory for the dynamics of the susceptible-infected-susceptible (SIS) epi- demic model on complex networks where dynamical correlations between connected vertices are taken into account by means of a pair approxima- tion [1]. This approach is an extension of the one-vertex QMF theory where the actual structure of network is explicitly included. We will present analytical expressions for the epidemic thresholds for the star and wheel graphs and for random regular networks. For random networks with a power law degree distribution, the thresholds were numerically determined via an eigenvalue problem. The pair and one-vertex QMF theories yield the same scaling for the thresholds as function of the net- work size. However, comparisons with quasi-stationary simulations [2] of the SIS dynamics on large networks show that the former is quantita- tively much more accurate than the latter. Our results demonstrate the central role played by dynamical correlations on the epidemic spreading. Finally, we will discuss the effects of outliers and cutoffs of the degree distribution in the epidemic thresholds. Our numerical results show the presence of a localized epidemics, which is sustained by outliers, and an endemic phase associated to the bulk of the network. For scale-free net- works (degree exponent γ < 3), we observed that the pair QMF theory predicts the correct scaling of the threshold against network size for both natural and structural cutoffs. However, for γ > 3 a hard-cutoff leads to the failure of the QMF theories. The numerical results are in better accordance with the mean-field recently theory proposed in Ref. [3]. [1] A. S. Mata, S. C. Ferreira, Pair quenched mean-field theory for the susceptible- infected-susceptible model on complex networks, preprint arXiv:1305.5153 (2013); [2] S. C. Ferreira, C. Castellano, R. Pastor-Satorras, Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of nu- merical and theoretical results, Phys. Rev. E 86, 041125 (2012); Abstracts: Oral Communications 57
[3] M. Bogu˜n´a, C. Castellano, R. Pastor-Satorras, The nature of epidemic thresholds in networks, preprint arXiv:1305.4819v1 (2013).
On generalisations of the log-Normal distribution by means of a new product definition in the Kapteyn process
S´ılvio M. Duarte Queir´os Centro Brasileiro de Pesquisas F´ısicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil In this presentation, I will discuss the modification of the Kapteyn mul- tiplicative process using the q-product of Borges [Physica A 340, 95 (2004)], which emerged within the Tsallis statistics framework. Depend- ing on the value of the index q a generalisation of the log-Normal distri- bution is yielded. Explicitly, the distribution increases the tail for small (when q<1) or large (when q>1) values of the variable upon analysis in relation to the standard log-Normal distribution, which is retrieved when q =1 and one has to the traditional Kapteyn multiplicative process. I will also introduce the main statistical features of this distribution as well as related random number generators. Lastly, I will illustrate the worthi- ness of this proposal by describing a set of variables of biological, namely the distribution of the chemical potential in metabolic networks and the capacity for distinguishing aerobic from anaerobic systems depending on the value of q.
Entropy for complex and non-ergodic systems, a derivation from first principles
Stefan Thurner & Rudolf Hanel Medical University of Vienna (MUV) – Vienna – Austria In their seminal works, Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs Abstracts: Oral Communications 58 type, S = i pi log pi. For non-ergodic systems the so called sepa- ration axiom− (Shannon-Khinchin axiom 4) is not valid. We show that whenever thisP axiom is violated the entropy takes a more general form, W Sc,d i Γ(d +1, 1 c log pi), where c and d are characteristic scaling exponents∝ that exist for− all systems that obey Shannon-Khinchin axioms 1-3. Γ(Pa,b) is the incomplete gamma function. The exponents (c,d) de- fine equivalence classes for all!, interacting and non interacting, systems and unambiguously characterize any statistical system in its thermody- namic limit. The proof is possible because of newly discovered scaling laws which any entropy has to fulfill, if the first three Shannon-Khinchin axioms hold [1]. (c,d) can be used to define equivalence classes of statis- tical systems. A series of known entropies can now be classified in terms of these equivalence classes. We show that the corresponding distribution functions are special forms of Lambert- exponentials containing – as W special cases – Boltzmann, stretched exponential, and Tsallis distribu- tions (power-laws). We show how the dependence of phase space volume W (N) on its size N, uniquely determines the exponents (c,d), [2]. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a generalized (non-additive) form. We show that generalized en- tropies can only exist when the dynamically (statistically) relevant frac- tion of degrees of freedom in the system vanishes in the thermodynamic limit [2]. These are systems where the bulk of the degrees of freedom is frozen and is practically statistically inactive. Systems governed by generalized entropies are therefore those whose phase space volume effec- tively collapses to a lower-dimensional ‘surface’. We explicitly illustrate the situation for binomial processes and argue that generalized entropies could be relevant for self-organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, in- stantons, etc., and for problems associated with anomalous diffusion[2]. In this contribution we largely follow the lines of thought presented in [1– 3]. [1] R. Hanel, S. Thurner, Europhys Lett. 93, 20006 (2011); [2] R. Hanel, S. Thurner, Europhys Lett. 96, 50003 (2011); [3] S. Thurner, R. Hanel, What do generalized entropies look like? An ax- iomatic approach for complex, non-ergodic systems, in Recent advances in Generalized Information Measures and Statistics, Bentham Science eBook, (in Abstracts: Oral Communications 59 production 2013).
Dielectric constant at the critical point
Marcelo Hidalgo & Sylvio Canuto Institute of Physics, Universidade de S˜ao Paulo (USP) – S˜ao Paulo – Brazil. The behavior of the dielectric constant around the critical point has been of interest for many years, with particular interest in the possible exis- tence of singularities [1–3]. In this work we use first-principle electronic structure calculations combining classical Monte Carlo simulations and density-functional quantum mechanical calculations to analyze the be- havior of the dielectric constant both at the critical point and around it. This combined use of molecular modeling and quantum mechanics (QM/MM) allows an accurate description giving numerical results for the static dielectric constant at the critical point in very good agreement with experiment, leading credence to the behavior of the calculated val- ues obtained around the critical density. Work supported by FAPESP, CNPq, CAPES and INCT-FCx. [1] G. Stell, J. S. Hoye, Phys. Rev. Lett. 33, 1268 (1974); [2] M. H. W. Chan, Phys. Rev. B 21, 1187 (1980); [3] C. E. Bertrand, J. V. Sengers, M. A. Anisimov, J. Pys. Chem. B 115, 14000 (2011).
Central limit behaviour of dynamical systems: Emergence of q-Gaussians and scaling laws
Ugur Tirnakli Department of Physics, Faculty of Science, Ege University – Izmir˙ – Turkey For deterministic dynamical systems, a central limit theorem is valid only if the system is sufficiently mixing. However, due to strong tempo- ral correlations, a standard central limit theorem is not valid when the system is in the vicinity of chaos threshold. We have shown [1,2] that the probability distribution of sums of iterates of the logistic map in the Abstracts: Oral Communications 60 vicinity of chaos threshold can be well approximated by a q-Gaussian. Then, recently, a generalized Huberman-Rudnick scaling law has been obtained for all periodic windows of the logistic map and robustness of the q-Gaussian probability distributions in the vicinity of chaos threshold has been shown [3]. Finally, relationships among correlation, fractality, Lyapunov divergence and q-Gaussian distributions have been numerically introduced [4]. The scaling arguments possessing the critical exponents between the size of the q-Gaussian and correlation, fractality, Lyapunov divergence are obtained for periodic windows (i.e., period 2, 3 and 5) of the logistic map as chaos threshold is approached [4]. All these findings can be though as new evidences supporting that the central limit behav- ior at the chaos threshold is given by a q-Gaussian. [1] U. Tirnakli, C. Beck, C. Tsallis, Phys. Rev. E 75, 040106(R) (2007); [2] U. Tirnakli, C. Tsallis, C. Beck, Phys. Rev. E 79, 056209 (2009); [3] O. Afsar, U. Tirnakli, EPL 101 20003 (2013); [4] O. Afsar, U. Tirnakli, in preperation (2013). Abstracts: Poster Sessions
No trivial extinctions transition in a two species population dynamics model Alexandre Souto Martinez & Fabiano Ribeiro & Brenno C. T. Cabella Universidade de S˜ao Paulo (USP) – S˜ao Paulo – Brazil The two-species population dynamics model is the simplest paradigm of inter- and intra-species interaction. Here, we present a generalized Lotka- Volterra model with intraspecific competition, which retrieves as particu- lar cases, some well known models. We identify the model generalization parameter with the environmental fractal dimension and the individu- als near and far con-specifics interaction range. The species inter-specific interaction parameters are not constrained and represent different ecolog- ical regimes. The asymptotic solutions stability analysis leads to a phase diagram in the parameter space representing the ecological regimes. In this diagram we call the attention to: a forbidden region in the mutual- ism regime and to the region with dependence on initial conditions, in the competition regime. Also, we have shed light on two types of preda- tion and competition: weak, if there are species coexistence, or strong, otherwise.
Non-Gaussian behavior in jamming / unjamming transition in dense granular materials Allbens P. F. Atman Departamento de F´ısica e Matem´atica, Centro Federal de Educa¸c˜ao Tecnol´ogica de Minas Gerais (CEFET-MG) – Minas Gerais – Brazil National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil Experiments of dense and disordered granular media were reported re- cently showing the jamming / unjamming transition. In the present work, Abstracts: Poster Sessions 62 we perform molecular dynamics simulations in order to assess both kine- matic and static features of jamming / unjamming transition. We study the statistics of the particles velocities and displacements to evince that both experiments and simulations present the same qualitative behavior. We observe that the probability density functions (PDF) of velocities de- viate from Gaussian depending on the packing fraction of the granular assembly. In order to quantify these deviations we consider a q-Gaussian (Tsallis) function to fit the PDF’s. The q-value can be an indication of the presence of long range correlations along the system. We com- pare the fitted PDF’s obtained with those obtained using the stretched exponential, and sketch some conclusions concerning the nature of the correlations along a granular confined flow.
Non extensive H-Theorem in general relativity Alyson Paulo Santos Universidade Federal do Rio Grande do Norte (UFRN) – Rio Grande do Norte – Brazil In this paper we have showed the nonextensive H-theorem in general relativity. For this purpose, we consider the prerrogatives of quantum statistics in the nonextensive formalism and relativistic kinetic theory in a scenario composed of a quantum gas isolated on a specific volume in the presence of a gravitacional field. We also determined, by equilibrium condition, the generalized stationary distributions of this gas.
Generalized complexity and classical-quantum transition Andres M. Kowalski Comisi´on de Investigaciones Cient´ıficas and Departamento de F´ısica-IFLP, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP) – La Plata – Argentina We investigate the classical limit of the dynamics of a semiclassical sys- tem that represents the interaction between matter and a given field. On Abstracts: Poster Sessions 63 using as a quantifier the q-Complexity, we find that it describes appropri- ately the quantum-classical transition, detecting the most salient details of the changeover. Additionally the q-Complexity results a better quan- tifier of the problem than the q-entropy, in the sense that the q-range is enlarged, describing the q-Complexity, the most important characteristics of the transition for all q-value. Keywords: Generalized entropy; Semi- classical theories; Quantum chaos; Statistical complexity. Email address: [email protected].
The transformation groupoid structure of the q-Gaussian family
Angel Akio Tateishi Universidade Estadual de Maring´a(UEM) – Paran´a– Brazil Groupoid theory plays an important role in physics since the beginnings of quantum mechanics. Recent developments in understanding symme- tries in complex dynamical systems underpin the growing importance of groupoid theory also for statistical mechanics. The q-Gaussian function is observed as the distribution function of many physical and biological systems and emerges naturally in the statistical mechanics of non-ergodic and complex systems. A number of dynamical systems are characterized by pairs and triples of q-Gaussians. The aim of this work is to relate these triples of q-Gaussians with different q-values, representing intrinsic symmetries of the dynamical system at hand, such that that any value of q can be mapped uniquely to any other value q′. We present a complete set of transformations of q-Gaussians by deriving a general map γqq′ that transforms normalizable q-Gaussian distributions into one another. We show that the action of γqq′ is a transformation groupoid. Abstracts: Poster Sessions 64
Classical and quantum harmonic oscillator with position-dependent mass
Bruno G. da Costa1,2 & Fabiano F. dos Santos1 & Ernesto P. Borges2,3 1Instituto Federal de Educa¸c˜ao, Ciˆencia e Tecnologia do Sert˜ao Pernambucano (IFSert˜ao-PE) – Pernambuco – Brazil 2Instituto de F´ısica, Universidade Federal da Bahia (UFBA) – Bahia – Brazil 3National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil Systems consisting of particles with position-dependent mass (PDM) have been discussed by several researchers since past few decades. Ap- plications of such systems may be found in semiconductor theory, 4He impurity in homogeneous liquid 3He, nonlinear optics, studies of in- version potential for NH3 in density functional theory (DFT), particle physics and astrophysics. Recently, Costa Filho et al. [EPL 101, 10009 (2013)] have introduced a generalized translation operator which pro- duces infinitesimal displacements related to the q-algebra, i.e., Tˆ (ε) x q | i≡ x + ε + γqxε , where γq (1 q)/ξ, q is a dimensionless parameter, and |ξ is a characteristici length.≡ This− operator leads to a generator operator of spatial translations corresponding to a position-dependent linear momen- tum given byp ˆq =(1+ˆ γqxˆ)ˆp, and consequently a particle with position- dependent mass. Through the inclusion of a q-exponential factor in the expression of Tˆq(ε), we re-obtain the deformed linear momentum opera- (1+ˆ γqxˆ)ˆp pˆ(1+ˆ γqxˆ) tor in a symmetrical form:p ˆq = 2 + 2 . The deformed position 1 operatorx ˆq = γq− ln(1+γqxˆ) is introduced so that it is canonically conju- gated with respect top ˆq. These operatorsx ˆq andp ˆq was originally used to solve problems of particles with position-dependent mass in the quantum formalism. Particularly, the canonical transformation (ˆx, pˆ) (ˆxq, pˆq) → 2 leads a particle with position-dependent mass m(x)= m/(1+ γqx) in a harmonic potential to a particle with constant mass in a Morse potential. Furthermore, since the operatorsx ˆq andp ˆq are Hermitian and canonically conjugated, we can analyze the classical analogue of quantum systems in- volving these dynamical variables. We revisit the problem of a position- dependent mass in a harmonic potential in both classical and quantum formalisms. The equations of motion in phase space (x,p) are expressed Abstracts: Poster Sessions 65 in terms of the generalized dual q-derivative D˜ x(t)= 1 dx . Specifi- γq,t 1+γqx dt cally, this oscillator with position-dependent mass is related to non-linear differential equations D˜ 2 x(t)= ω2x(t) and D˜ x(t)= ω √A2 x2, γq,t − 0 γq,t ± 0 − similar to the usual case, however, with the usual derivative replaced by deformed derivative. The analytical solution of these NLE led us to define new deformed trigonometric functions Sinq(u) and Cosq(u), such ˜ that Dγq,uSinqu = Cosqu and Dγq,uCosqu = Sinqu, which preserve the 2 2 − Pythagorean theorem Sinqu+Cosqu = 1. The trajectories in phase spaces (x,p)e and (xq,pq) are analyzed for different values of γq. Lastly, we com- pared the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.
Scaling functions for systems with finite range of interaction
Cesar Ivan Nunes Sampaio Filho Departamento de F´ısica, Universidade Federal do Cear´a(UFC) – Cear´a– Brazil We present a numerical determination of the scaling functions of the mag- netization, the susceptibility, and the Binder’s cumulant for two nonequi- librium model systems with varying range of interactions. We consider Monte Carlo simulations of the block voter model (BVM) on square lat- tices and of the majority-vote model (MVM) on random graphs. In both cases, the satisfactory data collapse obtained for several system sizes and interaction ranges supports the hypothesis that these functions are universal. Our analysis yields an accurate estimation of the long- range exponents, which govern the decay of the critical amplitudes with the range of interaction, and is consistent with the assumption that the static exponents are Ising-like for the BVM and classical for the MVM. Abstracts: Poster Sessions 66
A nonextensive approach to the stellar rotational evolution for F- and G-type stars Daniel Brito de Freitas Depart. de F´ısica Te´orica e Experimental (DFTE), Universidade Federal do Rio Grande do Norte (UFRN) – Rio Grande do Norte – Brazil The pioneering study by Skumanich (1972) showed that the rotational velocity of G-type Main-Sequence (MS) stars decreases with stellar age 1/2 according to v sin i t− . This relationship is consistent with simple theories of angularh i momentum ∝ loss from rotating stars, where an ion- ized wind is coupled to the star by a magnetic field. The present study introduces a new approach to the study of stellar rotational braking in unsaturated F and G type stars limited in age and mass, connecting angular momentum loss by magnetic stellar wind with Tsallis nonexten- sive statistical mechanics. As a result, we show that the rotation-age relationship can be well reproduced using a nonextensive approach from Tsallis nonextensive models. Here, the index q, which is related to the degree of nonextensivity, can be associated to the dynamo process and to magnetic field geometry, offering relevant information on the level of stellar magnetic braking for F- and G-type Main-Sequence stars.
A Comparison between methods for analyzing physiological time series
Diego Mateos1 & Pedro W. Lamberti1 & Steeve Zozor2,3 1Facultad de Astronom´ıa F´ısica y Matem´atica (FaMAF), National University of Cordoba (UNC) – C´ordoba – Argentina 2Department of Physics, National University of La Plata (UNLP) – La Plata – Argentina 3Gipsa-Lab – Grenoble – Francia Physiological registers, like EEG, ECG and blood pressure has been anal- ysed using differents statistical technique, many of them developed for time series. Recently this set of tools has been expanded by the inclusion Abstracts: Poster Sessions 67 of physical concept like chaos, complexity, criticality and others [1,3]. The use of these concepts has allowed a better understanding of the dynamical aspects behind the system originating the corresponding reg- isters. A very significant example is the association of chaotic behavior in ECG registers with some kind of cardiac disease [4]; or the appli- cation of wavelets entropies in the study of EEG register of epileptic patients [5]. We investigate different method of analysis in physiologic register, based on theoretical information quantities (entropy, Jensen- Shannon divergence), Band and Pompe permutation entropy [6] and the Lempel-Ziv complexity [7]. These methods have been applied in EEG registers, continuous monitoring Blood pressure and respiration registers. Even thought our results are preliminary we can arrive to some signif- icant conclusions about the ad-vantage of one method over the others, and we investigate the extraction of information clinically relevant from this analysis. [1] Chi-Sang Poon, Christopher K. Merrill, Decrease of cardiac chaos in con- gestive heart failure, Nature 389 (1997); [2] L. Glass, Synchronization and rhytmic processes in physiology, Nature 410 (2001); [3] C.-K. Peng, C.-C. Albert, Ary L. Goldberger, Statical physics approach to categorize biologic signals, CHAOS 17 (2007); [4] M. E. Pereyra, P. W. Lamberti, O. A. Rosso, Dynamical change detection on Eeg series: wavelet Jensen–Shannon divergence, Physica A (2006); [5] Hojjat Adeli, Samanwoy Ghosh-Dastidar, Nahid Dadmehr, A Wavelet- Chaos Methodology for Analysis of EEG and EEG Subbands to Detect Seizure and Epilepsy, IEEE transaction on Biomedical Engineering 54 (2007); [6] C. Bandt, B. Pompe, Permutation Entropy: A Natural Complexity Mea- sure for Time Series, Phys. Rev. Lett. (2002); [7] A. Lempel, J. Ziv, On the complexity of finite sequences, IEEE Transac- tions on Information Theory 22, 75–81 (1976). Abstracts: Poster Sessions 68
A Kramers-Moyal expansion approach to time series of the atmospheric temperature – A contribution to the discussion of the global weather change
Edson P. da Silva Department of Physics, Universidade Federal Rural do Rio de Janeiro (UFRRJ) – Rio de Janeiro – Brazil We investigate in an unified description, the dynamics of long and short time range of the fluctuation of the environment temperature presented by their statistics. We do that analyzing a real temperature time series, in a wide range of temporal scales to encompass both regimes. By means of Kramers-Moyal (KM) coefficients evaluated from empirical time series, we obtain the evolution equation for the probability density function (PDF) of temperature fluctuations. We also present asymptotic solutions for the timescale dependent equation that emerges from the empirical analysis.
Reactive strategies: The establishment of cooperation
Elton Jos´eda Silva J´unior Universidade Federal de Minas Gerais (UFMG) – Minas Gerais – Brazil. Individuals in nature, in many different populations, exhibit cooperative behaviour. The so called Prisoner’s dilemma is a game which is widely used to model this phenomena. Players in this game have two options: cooperation (C) or desertion (D). If there is only one round, deserting is the best option. But once the individuals meet each other several times, cooperative behaviour can emerge. Being p and q the probabilities of cooperating given that the opponent had cooperate and deserted in the last encounter, respectively, an infinity number of strategies is available. The time evolution of the fractions of individuals playing a given strategy is governed by the replicator equation. Since we have distinct versions for Abstracts: Poster Sessions 69 this equation and different ways to solve it (using continuous or discrete time approaches) we can obtain discordant outcomes. In this wor k we show that the usual results which is presented in literature (GTFT’s victory) is found only when we use the discretized version of the Maynard Smith’s replicator equation. In order to investigate the establishment of cooperation, we also analyse the flux diagram of initial conditions for a few strategies and study what happens when new strategies are added in the game, starting from the point in which all strategies are equally populated.
Generalized space and linear momentum operators in quantum mechanics
Bruno G. da Costa1 & Ernesto P. Borges2,3 1Instituto Federal de Educa¸c˜ao, Ciˆencia e Tecnologia do Sert˜ao Pernambucano (IFSert˜ao-PE) – Pernambuco – Brazil 2Instituto de F´ısica, Universidade Federal da Bahia (UFBA) – Bahia – Brazil 3National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil
We propose a generalized space operatorx ˆq for which it is valid the canonical commutation relation with the generalized momentum oper- atorp ˆq recently introduced by Costa Filho et al. [Phys. Rev. A 84, 050102(R) (2011)]. These operators are related to infinitesimal transla- tions x x + ε + γqxε , where γq (1 q)/ξ, q is a dimensionless parameter,| i→| and ξ is a characteristici length.≡ − This generalized linear mo- mentum operator is position-dependent and, accordingly, corresponds to a position-dependent mass particle. Furthermore, (ˆx, pˆ) (ˆxq, pˆq) is a canonical transformation with the classical analogue that→ leads the Hamiltonian K(xq,pq) of a particle with constant mass m in a conserva- tive force field of a deformed phase space (xq,pq) into the Hamiltonian H(x,p) of a position-dependent mass particle with effective mass function 2 m(x) = m/(1 + γqx) . Time evolution of the deformed position xq may be conveniently expressed in terms of the generalized dual q-derivative dxq ˜ acting upon the usual position x, according to dt = Dγq,tx, with the dual q-derivative operator defined as D˜ f(u) = 1 df . A position- γq,u 1+γqu du Abstracts: Poster Sessions 70 dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Fractional diffusion equation, surface effects and anomalous diffusion
E. K. Lenzi1,3 & A. A. Tateishi1 & F. M. Santana1 & M. A. F. dos Santos1 & H. V. Ribeiro1 & M. K. Lenzi2 1Departamento de F´ısica, Universidade Estadual de Maring´a (UEM) – Paran´a– Brazil 2Departamento de Engenharia Qu´ımica, Universidade Federal do Paran´a (UFPR), Setor de Tecnologia – Paran´a– Brazil 3National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil We investigate time dependent solutions for a system in a semi-infinite region and governed by a fractional diffusion equation. We also consider that the surface which delimit the system can adsorb and desorb particles with determinate rates. This process of adsorption-desorption is simu- lated by using integro-differential time dependent boundary condition on this surface. The solutions are obtained by using the Green function ap- proach and shows an anomalous spreading which can be related to an anomalous diffusion.
Scaling exponents of rough surfaces generated by damage spreading in the Ising model
Felipe Aguiar Severino dos Santos & Everaldo Arashiro Universidade Federal de Ouro Preto (UFOP) – Minas Gerais – Brazil We carry out a study of the phase transitions in the damage spreading in the one-dimensional Ising model under a dynamic introduced by Hin- richsen and Domany (HD) and mapping of the spin configurations to a solid-on-solid growth model, resulting in an aggregate which is compact (no vacancies) and without surface overhangs. A system is said to exhibit Abstracts: Poster Sessions 71 damage spreading (DS) if the“distance”between two of its replicas, that evolve under the same thermal noise but from slightly different initial conditions, increases with time. The dynamic introduced by Hinrichsen and Domany exhibit nondirected percolation universality class contin- uous phase transitions to absorbing states, exhibit parity conservation (PC) law of kinks. The kinks (00’s and 11’s) of these models exhibit mod 2 parity conservation and the absorbing state is doubly degener- ated. They are characterized by different exponents which are related to the PC universality class. We have obtained such exponents through M onte Carlo smilulations, variating the lattice size at critical probability. We estimated the growth exponent betaw at short times, such as, other critical exponents associated to the surface growth (teta and z). Our results are in good agreement with those expected for PC universality class. The critical roughening exponents, expected to belong to the PC universality class, were measured using power law relations valid at crit- icality. Supported by Capes, CNPq and Fapemig. [1] A. P. F. Atman, R. Dickman, J. G. Moreira, Phys. Rev. E 66, 016113 (2002); [2] S. A. Kauffman, J. Theor. Biol. 22, 437 (1969); [3] H. Hinrichsen, E. Domany, Phys. Rev. E 56, 94 (1997).
Permutation quantifiers and the fine structure on the chaotic attractors.
Felipe Olivares1 & Angel Plastino2 & Osvaldo Rosso3,4 1Universidad Nacional de La Plata (UNLP) – La Plata – Argentina 2Instituto de F´ısica, National University La Plata (UNLP) & National Research Council (CONICET) – La Plata – Argentina 3Laboratorio de Sistemas Complejos, Facultad de Ingenier´ıa, Universidad de Buenos Aires (UBA) – Capital Federal – Argentina 4LaCCAN/CPMAT - Instituto de Computa¸c˜ao, Universidade Federal de Alagoas (UFAL) – Alagoas – Brazil We highlight the potentiality of a special Information Theory approach in order to unravel the intrincates of nonlinear dynamics. Information quantifiers as the Shannon entropy, statistical complexity and Fisher in- formation are functionals that characterizes the probability distribution Abstracts: Poster Sessions 72
P associated to the time series generated by a given dynamical system. The adequate way of picking up such distribution is achieved by the Bandt and pompe metodology, which is one of the most simple symbol- ization techniques available and takes into account time – causality in the concomitant process. In this communication we introduce two rep- resentation spaces called causality entropy-complexity information plane ( ), which quantifies global features, as the presence of correlational structuresH×C and, the causality entropy-Fisher information plane ( ) that measures local features. These two informational planes becomeH × F a new tool to characterize a time series generated by a dynamical systems or experimental measurements. We studied 3 routes to chaos namely period doubling, tangent bifurcation and hopf bifurcation as a funtion of a control parameter, simulated by time series obtained from two discrete chaotic systems: logistic map and delayed logistic map. The analysis in both causality planes and provide a characterization of the intrinsic informationH×C of the maps,H × independently F from the control parameter. The plane shows a specific behavior for each kind of routes to chaos.H At× F this point we are able to differentiate between a period doubling tree; intermittency behavior ocurring before the tangent bifurcation; periodic attractos; and quasiperiodic orbits generated by the delayed logisctic map after a critical value rH of the parameter (Hopf bifurcation). This characterization comes in what we call a dynamic fea- ture plane-topography map, , because the local sentitivity of the Fisher information quantifier.H On × F the other hand, the characterization given by the plane locates all the dynamics on the curve of maxi- H×C mum complexity, independely of the underlying phenomenon in the time series. Thus we are not able to identificate the differences between the dynamics under analysis. This last characterization is consistent with the quantification given by the Lyapunov exponents. Finally a study of the evolution of the information quantifiers as a function of the sam- pling time τ used when we construct the PDF, allows us to infer usefull information about the characteristic temporal scales of the underlying dynamics of the temporal series. More precisely, we are able to identify between periodic and quasiperiodic orbits. A quasiperiodic motion can be thought as a mixture of periodic orbits with different fundamental frecuencies. We are able to characterize qualitative and quantitative the period of these movements. Abstracts: Poster Sessions 73
Free energy evaluation in polymer translocation via Jarzynski equality
Felipe Mondaini Centro Federal de Educa¸c˜ao Tecnol´ogica (CEFET-RJ) – Rio de Janeiro – Brazil The phenomenon of polymer translocation through membrane pores has received a great deal of attention in recent years. Important issues are related to the translocation of complex biomolecules in the methabolism of living cells, and, on the technological forefront, to developments in the fields of targeted drug/gene delivery and DNA sequencing. In studying the thermodynamic state of a physical system, the free energy F is a quantity of fundamental importance. It describes the equilibrium prop- erties of systems that may exchange energy with their environments. Formally, it is related to the internal energy, U, by a Legendre transform F = U TS, where T is the temperature and S the entropy. The free energy is− a state function and hence, for any process connecting two equi- librium states, the respective change of the free energy F = U TS, solely depends on the final and initial states without regard to the− particular process connecting them. In contrast, the work W done on the system and the heat Q exchanged with the environment are process-dependent. Yet, their sum yielding the change in internal energy, U = W + Q, does not depend on the details of the path connecting the final with the initial state. Recently, Jarzynski found a relation between the path dependent work and the path independent free energy change in terms βW β∆F of the following rule: e− = e− . The process from which this h i work results, starts out in a state of thermal equilibrium at temperature 1 T = (kB)− , and is induced by the action of forces, or more generally by changes of parameters characterizing the Hamiltonian of the consid- ered system. In this work we compare the results obtained by Jarzyn- ski Equality with those established by Muthukumar in the estimation of the free energy in the polymer translocation problem. Keywords: Free Energy, Jarzynski Equality, Polymer Translocation. Email address: [email protected]. Abstracts: Poster Sessions 74 Growing jackpot and persistence in lottery winners
Fernando J. Antˆonio & R. S. Mendes & A. I. da Silva & S. Picoli Jr Departamento de F´ısica, Universidade Estadual de Maring´a (UEM) – Paran´a– Brazil National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil Historically, lottery seems to be the most famous branch among all the games of chances playing a relevant role in the behaviour of many indi- viduals. In this work, we analyze data from Mega-Sena, the major lottery in Brazil. We show that while the size of the expected jackpot is growing, the demand for lottery tickets may grow exponentially. In addition, we find that the number of winners exhibits temporal persistent behavior despite unbiased draws. We propose a straightforward model grounded on the rolling-over feature of lottery that exhibits a persistent behaviour similar to those observed in the empirical data. Our results are consis- tent with the fact that the expectation of being awarded with money may drive human actions. In this framework, the desire for the jackpot (related to the increase in the sales of tickets) could be a mechanism to generate correlations in an apparently random scenario. Keywords: Au- tocorrelation, Human Behaviour, Rollover, Jackpot. Correspondence and requests for materials should be addressed to F.J.A. ([email protected]).
First passage time for a diffusive process under a geometric constraint
A. A. Tateishi1,2 & Fl´avio S. Michels1 & M. A. F. dos Santos1 & E. K. Lenzi1 & H. V. Ribeiro1 1Departamento de F´ısica, Universidade Estadual de Maring´a (UEM) – Paran´a– Brazil 2Section for Science of Complex Systems, Medical University of Vienna – Vienna – Austria We investigate the solutions, survival probability, and first passage time for a two dimensional diffusive process subjected to the geometric con- straints of a backbone structure. We consider this process governed by a Abstracts: Poster Sessions 75 fractional Fokker-Planck equation by taking into account the boundary conditions ρ(0,y; t) = ρ( ,y; t) = 0, ρ(x, ; t) = 0, and an arbitrary initial condition. Our results∞ show an anomalous±∞ spreading and, con- sequently, a nonusual behavior for the survival probability and for the first passage time distribution that may be characterized by different regimes. In addition, depending on the choice of the parameters present in the fractional Fokker-Plack equation, the survival probability indicates that part of the system may be trapped in the branches of the backbone structure.
Alternative measures for biospeckle image analysis
Fortunato Silva de Menezes Universidade Federal de Lavras (UFLA) – Minas Gerais – Brazil Biospeckle is a technique whose purpose is to observe and study the un- derlying activity of some material. It has its roots in optical physics, and its first step is an image acquisition process that produces a video se- quence of the reflection of a laser. The video content can be analyzed to have an interpretation of the activity of the observed material. The liter- ature on this subject presents several different measures for analyzing the video sequence. Three of the most popular measures are the generalized difference (GD), the weighted generalized difference (WGD), and Fujii’s method. These measures have drawbacks such as high computation time or limited visual quality of the results. In this paper, we propose (i) an alternative O n algorithm for the computation of the GD, (ii) an alterna- tive measure based on the GD, (iii) an alternative measure based on the WGD, and (iv) a generalized definition of the Fujii’s method with bet- ter visual quality. We discuss the similarities between the new measures and the existent ones, showing when they are applicable. We prove the gain in time computation. The proposed measures will help researchers to gain time during their research and to be able to develop faster tools based on biospeckle application. Abstracts: Poster Sessions 76
Control of centrifugal fingering via a variable interfacial tension approach
Francisco Rocha & Jos´eA. Miranda Universidade Federal de Pernambuco (UFPE) – Pernambuco – Brazil We study the centrifugal fingering instabilities that occur in rotating Hele-Shaw cells containing two different fluids. A weakly nonlinear anal- ysis of the problem is performed, considering that the surface tension be- tween the rotating fluids changes with the local curvature of the interface. It is shown that the coupling between the contact angle and the variable interfacial tension permits the control of the interface disturbances. As a result, linear perturbations and nonlinear finger competition phenomena can be properly controlled, and suppressed.
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
Gabriel Dias Carvalho & Jos´eA. Miranda & Hermes Gadˆelha Departamento de F´ısica, Universidade Federal de Pernambuco (UFPE) – Pernambuco – Brazil We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the in- terface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that nonlinear effects significantly affect the ultimate shape of the pattern-forming structures. Abstracts: Poster Sessions 77
Entropy production in systems described by a master equation
Gabriela A. Casas† & Fernando D. Nobre & Evaldo M. F. Curado Centro Brasileiro de Pesquisas F´ısicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil The H-theorem, and consequently the second law of thermodynamics, which states that the entropy of an isolated system always increases for irreversible processes, leads to the interesting phenomenon of entropy production. Within the statistical definition of entropy, the entropy production depends directly on the time derivative of the correspond- ing probability; for this purpose one may use, e.g., the Boltzmann, or Fokker-Planck equations in the case of continuous probabilities, or the master equation, when dealing with discrete probabilities. In the present work we study the entropy time rate of systems described by master equations, using generalized entropic forms. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings, are studied. Some examples of known generalized entropic forms are considered, and particularly, the expression for the production of the Boltzmann-Gibbs entropy, obtained from the standard master equation, is recovered as particular case. Since nonlinear effects, introduced through the transition probabilities of the master equation, are relevant for several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applica- ble to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies. Keywords: Entropy Production, Master Equation, Nonextensive Thermostatistics. †Email address: [email protected]. Abstracts: Poster Sessions 78
Finite baths for Tsallis statistics: a rigorous approach
Gokhan Baris Bagci Physics Department, Ege University – Izmir˙ – Turkey
Radial viscous fingering in yield stress fluids: Onset of pattern formation
Jo˜ao V. Fontana & Jos´eA. Miranda Dpto. de F´ısica, Universidade Federal de Pernambuco (UFPE) – Pernambuco – Brazil We report analytical results for the development of interfacial instabili- ties in a radial Hele-Shaw cell in which a yield stress fluid is pushed by a Newtonian fluid of negligible viscosity. By dealing with a gap averag- ing of the Navier-Stokes equation, we derive a Darcy-law-like equation for the problem, valid in the regime of high viscosity compared to yield stress effects. A mode-coupling approach is executed to examine the mor- phological features of the fluid-fluid interface at the onset of nonlinearity. Within this context, mechanisms for explaining the rising of tip-splitting, side-branching and competition events are proposed for lifting and inject- ing Hele-Shaw flow.
Nonextensive thermostatistic properties of compact stars
Jos´eA. C. Nogales & Karen Luz-Burgoa Universidade Federal de Lavras (UFLA) – Minas Gerais – Brazil In this work we discuss relevant aspects of the δ-thermostatistical treat- ment for an Fermi system in the context of generalized entropy proposed Abstracts: Poster Sessions 79 recently by C. Tsallis and L.J.L. Cirto (Eur. Phys. J. C 73, 2487 (2013)). After that, we analyzed properties of neutron and white dwarf stars in the framework of nonextensive δ-statistical mechanics. We show that nonextensive statistical effects could play a interesting role in the struc- ture and in the evolution of the compact stars for small deviations from the standard Boltzmann-Gibbs statistics.
Anomalous g-factors for charged leptons in a fractional coarse-grained approach
1, 2,⋆ Jos´eWeberszpil † & J. A. Helay¨el-Neto 1Universidade Federal Rural do Rio de Janeiro (UFRRJ) – Rio de Janeiro – Brasil 2Centro Brasileiro de Pesquisas F´ısicas (CBPF) – Rio de Janeiro – Brasil In this work, we investigate aspects of the electron, muon and tau gy- romagnetic ratios (g factor) in a fractional coarse-grained scenario, by adopting a Modified− Riemann-Liouville (MRL) fractional calculus. We point out the possibility of mapping the experimental values of the specie’s g factors into a theoretical parameter which accounts for frac- tionality, without− computing higher-order QED calculations. We wish to understand whether the value of (g 2) may be traced back to a fraction- − ality of space-time.The justification for the difference between the experi- mental and the theoretical value g = 2 stemming from the Dirac equation is given in the terms of the complexity of the interactions of the charged leptons, considered as pseudo-particles and ”dressed” by the interactions and the medium. Stepwise, we build up a fractional Dirac equation from the fractional Weyl equation that, on the other hand, was formulated exclusively in terms of the helicity operator. From the fractional angu- lar momentum algebra, in a coarse-grained scenario, we work out the eigenvalues of the spin operator. Based on the standard electromagnetic current, as an analogy case, we write down a fractional Lagrangian den- sity, with the electromagnetic field minimally coupled to the particular charged lepton. We then study a fractional gauge-like invariance symme- try, formulate the covariant fractional derivative and propose the spinor field transformation. Finally, by taking the non-relativistic regime of the Abstracts: Poster Sessions 80 fractional Dirac equation, the fractional Pauli equation is obtained and, from that, an explicit expression for the fractional g factor comes out that is compared with the experimental CODATA value.− Our claim is that the different lepton species must probe space-time by experiencing different fractionalities, once the latter may be associated to the dress- ing of the particles and, then, to the effective interactions of the differ- ent families with the medium. Email addresses: †[email protected], ⋆[email protected].
Controlling the range of interactions in the classical inertial Heisenberg model
Leonardo J. L. Cirto1 & Leonardo S. Lima2 & Fernando D. Nobre1,3 1Centro Brasileiro de Pesquisas F´ısicas (CBPF) – Rio de Janeiro – Brazil 2Universidade Federal de Minas Gerais (UFMG) – Minas Gerais – Brazil 3National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil Numerical results on the ferromagnetic Heisenberg model characterized by interactions with a variable range are presented. The system is de- fined as an ensemble of N localized classical Heisenberg rotators, coupled through interactions that decay with distance as 1/r α (α 0). By intro- ducing a kinetic term, the total energy becomes a sum of≥ the interaction and kinetic terms, in such a way to present its own dynamics, through a Hamiltonian formulation. The Hamiltonian is given by
1 N 1 N N 1 S S 1 N N 1 = L 2 + − i · j N = , H 2 i r α N r α i = 1 2N i = 1 j = i ij i = 1 j = i ij ! X X X6 X X6 e where we are assuminge a unit moment of inertia, Li represents the angu- lar momentum, and Si is a classical Heisenberg spin variable (defined in a sphere of unit radius). The spins are disposed along a ring, such that rij measures the minimum distance between rotators i and j, whereas the pa- rameter α allows one to control the interaction range. The particular case α = 0 (the fully coupled limit) has been previously studied in Ref. [1], and in the α limit one recovers the well-known one-dimensional → ∞ Abstracts: Poster Sessions 81 nearest-neighbour-interaction model. Herein we will be interested in the cases α > 0. We carried out microcanonical molecular-dynamics sim- ulations using the above Hamiltonian, focusing mainly in the study of metastable, or quasi-stationary states (QSS). Our results suggest that, for α< 1 (long-range interactions), the order in which the N and t limits are considered becomes important. Specifically,→ if ∞ we let N→ ∞ first, the system remains trapped in the QSS, never reaching the final→ Boltzmann-Gibbs ∞ equilibrium state. [1] F. D. Nobre, C. Tsallis, Phys. Rev. E 68, 036115 (2003).
Synchronization as a mechanism for protein folding Leandro Prade Nadaletti Graduate School and Research in Engineering (COPPE), Federal University of Rio de Janeiro (UFRJ) – Rio de Janeiro – Brazil Biochemical reactions in cells require that proteins adopt a specific con- formation in their native state. Experimental and theoretical studies con- ducted over recent decades have not fully explained the folding phenom- ena, despite significant advances in structural biology. Different models such as diffusion-collision and nucleation-condensation have been used to unravel how secondary and tertiary structures form during protein folding. Although such models enhance our understanding of the prob- lem, we have still not identified a simple mechanism based on physical principles that provide an accurate description of kinetics and thermo- dynamics for such phenomena. In this study, we introduce the hypoth- esis that the synchronization of the amino acids dynamics through the cooperative movements of the peptide planes along the backbone is a mechanism that adequately explains how a protein rapidly adopts a spe- cific three-dimensional structure. Synchronization is the ability for self- organization, wherein two or more self-sustaining dynamic systems adjust their rhythms to adopt coordinated behaviour through a low-intensity mutual influence. Such non-linear phenomena are widespread in nature and are applied in different fields of study, such as modelling cardiac cell behaviour in biology, and superconductors in physics, through Josephson junction arrays Proteins are chains of 20 different types of amino acids. Each amino acid has two degrees of freedom, and the angles of rotation Abstracts: Poster Sessions 82 around the N-Cα and Cα-C bonds are φ and ψ, respectively. Conversely, the peptide bond has a partial double bond character, which restricts free rotation around the N-C bond and causes H-N-C-O atoms to arrange in a conformation that defines the peptide or amide plane. The individual behavior of the peptide plane is expressed by the variation in the angles ψ of the i th amino acid and φ of the i+1th amino acid, which identifies such a structure as an oscillating system. Therefore, we adopted a simpli- fied representation of a protein backbone to describe its conformational dynamics, where the N peptide planes were idealized as oscillators. We draw a parallel between the folding process and dynamics for a network of coupled oscillators described by the Kuramoto model to illustrate the inherent concepts of the new proposed model. Based on the Kuramoto model, the stimulus for synchronization over a specific amino acid is not pre-determined because it arises from the interactions between the set of amino acids, constituting a typical case of self-organization. Thus, the native protein structure forms due to the mean-field forces acting on a specific amino acid sequence. Defining such forces can improve the prediction of the protein structure from sequence alone. In that sense, equivalent forces generated by homologous proteins, which evolved from a common ancestor, may explain the success of homology structural mod- eling. Likewise, changes in the composition of the forces caused, for ex- ample, by binding could explain the protein conformational changes seen in distant parts of the polypeptide chain, associated with the allosteric effect. We further expected that thoroughly understanding synchroniza- tion may facilitate control over the folding process and help to predict a protein’s native structure from its amino acid sequence. Abstracts: Poster Sessions 83
Ion-acoustic double-layers in magnetized plasmas with nonthermal electrons Luciana A. Rios1,3 & Ricardo M. O. Galv˜ao2,3 1Centro Brasileiro de Pesquisas Fisicas (CBPF) – Rio de Janeiro – Brazil 2Universidade de S˜ao Paulo (USP) – S˜ao Paulo – Brazil 3National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil A double layer (DL) consists of a positive/negative Debye sheath, con- necting two quasineutral regions of a plasma. These nonlinear structures can be found in a variety of plasmas, from discharge tubes to space plas- mas. It has applications to plasma processing and space propulsion [1], and its concept is also important for areas such as applied geophysics. The best known of these structures is the strong Langmuir DL, which is characterized by two counterstreaming plasmas, carrying a large electric current across the DL. The current-free double layer (CFDL) constitutes a different group, for which there is no trapped ion population. A DL may be regarded as a BGK equilibrium in some cases, for which certain conditions must be fulfilled. It is worth mentioning that in general the plasma distributions near a DL are strongly non-Maxwellian [2], with long tails observed in some cases [3]. In the present work we investigate a different class of double layers, the ion-acoustic double layers (non-BGK). It is believed that these structures are responsible for the acceleration of auroral electrons, for exa mple [4]. Considering that the plasma distributions near a DL are usually strongly non-Maxwellian, as mentioned before, we assume that the hot electron population is modeled via a κ distribution function [5]. The family of κ distributions has been proved to be appropriate for modeling non- Maxwellian plasmas. In its reduced form, the standard κ distribution is equivalent to the distribution function obtained from the maximization of the Tsallis entropy, the q distribution [6]. The parameters κ and q measure the deviation from the Maxwellian equilibrium (‘nonthermality’) and are related by the expression κ =1/(1 q). − − Here the existence of ion-acoustic double layers in magnetized two- electron plasmas is investigated. The influence of the magnetic field on Abstracts: Poster Sessions 84 the existence and structure of small amplitude DLs is analyzed, as well as the effects of quasineutrality and nonthermality. A comparison with previous works is also presented. [1] C. Charles, Plasma Sources Sci. Technol. 16, R1 (2007); [2] L. P. Block, Astrophys. Space Sci. 55, 59 (1978); [3] G. Hairepatian, R. L. Stenzel, Phys. Rev. Lett. 65, 175 (1990); [4] T. Sato, H. Okuda, Phys. Rev. Lett. 44, 740 (1980), T. Sato, H. Okuda, J. Geophys. Res. 86, 3357 (1981); [5] V. M. Vasyliunas, J. Geophys. Res. 73, 2839 (1968); [6] C. Tsallis, J. Stat. Phys. 52, 479 (1988), C. Tsallis, Physica A 221, 277 (1995).
Scaling laws in the dynamics of crime growth rate
⋆ Luiz G. A. Alves† & Haroldo V. Ribeiro & Renio S. Mendes‡ Departamento de F´ısica, Universidade Estadual de Maring´a (UEM) – Paran´a– Brazil National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil The increasing number of crimes in areas with large concentrations of peo- ple have made cities one of the main sources of violence. Understanding characteristics of how crime rate expands and its relations with the cities size goes beyond an academic question, being a central issue for contem- porary society. Here, we characterize and analyze quantitative aspects of murders in the period from 1980 to 2009 in Brazilian cities. We find that the distribution of the annual, biannual and triannual logarithmic homi- cide growth rates exhibit the same functional form for distinct scales, that is, a scale invariant behavior. We also identify asymptotic power-law de- cay relations between the standard deviations of these three growth rates and the initial size. Further, we discuss similarities with complex orga- ⋆ nizations. Email addresses: †[email protected], [email protected], ‡[email protected]. Abstracts: Poster Sessions 85
Nonlinear diffusion equation, solutions and Tsallis framework
E. K. Lenzi & Maike A. F. dos Santos & F. S. Michels & L. R. Evangelista & R. S. Mendes Departamento de F´ısica, Universidade Estadual de Maring´a (UEM) – Paran´a– Brazil We investigate the solutions of a generalized diffusion equation which contains nonlinear terms in presence of external forces and reaction terms. The solutions found here are expressed in terms of the q-exponentials functions present in the Tsallis framework and can have a compact or long tail behavior. For the last case, in the asymptotic limit, these solutions can be connected with the L´evy distributions. In addition, from the results presented here a rich class of diffusive processes, including normal and anomalous ones, can be obtained.
Boolean network model for cancer pathways: predicting carcinogenesis and target therapy outcomes
1,2, 1 Marcelo L. Martins † & Herman F. Fumi˜a 1Departamento de F´ısica, Universidade Federal de Vi¸cosa (UFV) – Minas Gerais – Brazil 2National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil A Boolean dynamical system integrating the main signaling pathways involved in cancer is constructed based on the currently known protein- protein interaction network [1–3]. This system exhibits stationary pro- tein activation patterns — attractors — dependent on the cell’s microen- vironment. These dynamical attractors were determined through simu- lations and their stabilities against mutations were tested. In a higher hierarchical level, it was possible to group the network attractors into Abstracts: Poster Sessions 86 distinct cell phenotypes and determine driver mutations that promote phenotypic transitions. Such drivers are in agreement with those pointed out by diverse census of cancer genes recently performed for several hu- man cancers. Furthermore, our results demonstrate that cell phenotypes can evolve towards full malignancy through distinct sequences of accu- mulated mutations. In particular, the network model supports routes of carcinogenesis known for some tumor types. Finally, the Boolean net- work model is employed to evaluate the outcome of molecularly targeted cancer therapies. [1] B. Vogelstein, K. W. Kinzel, Cancer genes and the pathways they control, Nat. Med. 10(8), 789–799 (2004); [2] R. Weinberg, The Biology of Cancer (Garland Science, New York, 2007); [3] KEGG Pathway database, http://www.genome.jp/kegg/pathway.html. †Email address: [email protected].
Classical field theory for a nonlinear Schroedinger equation
Fernando D. Nobre & Marco A. Rego Monteiro & Constantino Tsallis Centro Brasileiro de Pesquisas Fisicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil
An exact classical field theory, for a recently proposed nonlinear general- ization of the Schroedinger equation, is presented. In this generalization, a nonlinearity depending on an index q appears in the kinetic term, such that the free-particle linear Schroedinger equation is recovered in the limit q 1. It is shown that besides the usual Ψ(x,t), a new field Φ(x,t) → must be introduced, which becomes Ψ∗(x,t) only when q 1. In analogy → to the linear case, ρ(x,t)=1/(2V )[Ψ(x,t)Φ(x,t)+Ψ∗(x,t)Φ∗(x,t)] is interpreted as the probability density for finding the particle at time t, in a given position x inside an arbitrary finite volume V , for any q. The possible physical consequences are discussed, and in particular, the im- portant property that the fields Ψ(x,t) and Φ(x,t) do not interact with light. Abstracts: Poster Sessions 87 Overdamped motion of interacting particles in general confining potentials: Time-dependent and stationary-state analyses
Mauricio S. Ribeiro & Fernando D. Nobre & Evaldo M. F. Curado Centro Brasileiro de Pesquisas F´ısicas (CBPF) & National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil
By comparing numerical and analytical results, it is shown that a sys- tem of interacting particles under overdamped motion is very well de- scribed by a nonlinear Fokker-Planck equation, which can be associated with nonextensive statistical mechanics. The particle-particle interac- tions considered are repulsive, motivated by three different physical sit- uations: (i) modified Bessel function, commonly used in vortex-vortex interactions, relevant for the flux-front penetration in disordered type- II superconductors; (ii) Yukawa-like forces, useful for charged particles in plasma, or colloidal suspensions; (iii) derived from a Gaussian po- tential, common in complex fluids, like polymer chains dispersed in a solvent. Moreover, the system is subjected to a general confining po- tential, φ(x)=(α x z)/z (α > 0,z > 1), so that an stationary state is reached after a sufficiently| | long time. Recent numerical and analytical investigations, considering interactions of type (i) and a harmonic con- fining potential (z = 2), have shown strong evidence that a q-Gaussian distribution, P (x,t), with q = 0, describes appropriately the particle po- sitions during their time evolution, as well as in their stationary state. Herein we reinforce further the connection with nonextensive statistical mechanics, by presenting numerical evidence showing that: (a) In the case z = 2, different particle-particle interactions only modify the dif- fusion parameter D of the nonlinear Fokker-Planck equation; (b) For z = 2, all cases investigated fit well the analytical stationary solution 6 Pst(x), given in terms of a q-exponential (with the same index q = 0) of the general external potential φ(x). In this later case, we propose an approximate time-dependent P (x,t) (not known analytically for z = 2), which is in very good agreement with the simulations for a large range6 of times, including the approach to the stationary state. Abstracts: Poster Sessions 88 q-Statistics modelling NMR decay of unconsolidated porous media
Maury D. Correia1,2 & Jo˜ao P. Sinnecker1 & Roberto Sarthour1 & Alexandre M. Souza1 & Ivan S. Oliveira1 1Centro Brasileiro de Pesquisas F´ısicas (CBPF) – Rio de Janeiro – Brazil 2Centro de Pesquisas Leopoldo Miguez de Mello (CENPES), Petr´oleo Brasileiro S.A. (PETROBRAS) – Rio de Janeiro – Brazil The knowledge of hydrogen spin relaxation in porous media is of great interest in the oil industry and science. In this work we propose a analyti- cal statistical function for pore size distribution, such that we can predict the T2 distribution for a theoretical model of porous media. Applying this model to NMR transverse relaxation data, for real unconsolidated porous media, we can estimate the statistical parameters and derive the T2 and pore size distribution. Our model with two q-exponential proved to be superior to Tikhonov inversion with one thousand of exponential functions mostly for long relaxation time and computational cost.
A representation of the Dirac delta based on the q-exponential function Max J´auregui & Constantino Tsallis Centro Brasileiro de Pesquisas F´ısicas (CBPF) & National Institute for Science and Technology in Complex Systems (INCT-SC) – Rio de Janeiro – Brazil It is known that the Dirac delta function, δ(x), can be represented by (1/2π) ∞ eikxdk. This representation is closely related to the definitions of the Fourier−∞ transform and its inverse. With the development of the R nonextensive statistical mechanics, generalisations of the logarithm and the exponential function were conveniently done, resulting in the so-called q-logarithm and q-exponential function. These ‘q-generalised’ functions can be used to generalise other definitions and theorems. Thus we already have the q-Fourier transform and the q-central limit theorem. We show here that there exists a ‘q-generalised’ version of the representation of the Dirac delta shown above, which is based on the q-exponential function [1]. Moreover, we use this fact to find a formula that enables us to find a Abstracts: Poster Sessions 89 function f(x) from the q-Fourier transform of f(x + y), where y is an arbitrary value of the domain of f [2]. This formula can be useful since the q-Fourier transform is not invertible as was shown by Hilhorst (2010). [1] M. Jauregui, C. Tsallis, New representations of π and Dirac delta using the nonextensive-statistical-mechanics q-exponential function, J. Math. Physics 51, 063304 (2010); [2] M. Jauregui, C. Tsallis, q-generalization of the inverse Fourier transform, Phys. Lett. A 375, 2085 (2011).
Generalized information deficit and quantum discord in spin chains
Norma Canosa & L. Ciliberti & R. Rossignoli Departamento de F´ısica-IFLP, Universidad Nacional de La Plata (UNLP) – La Plata – Argentina We examine the quantum correlations of spin pairs in spin 1/2 chains in an applied transverse field B, through the analysis of the quantum discord and the generalized information deficit based on general entropic forms. The latter contains, as particular cases, the von Neumann based one-way information deficit, the geometric discord and the q-discord. It is shown [1] that all these quantities provide the same qualitative information. In the case of Heisenberg-type XY chains, they all reach full range for B Role of viscous friction in the reverse rotation of a disk Pablo de Castro & Fernando Parisio Universidade Federal de Pernambuco (UFPE) – Pernambuco – Brazil The mechanical response of a circularly driven disk in a dissipative medium is considered. We focus on the role played by viscous friction in the spin- ning motion of the disk, especially on the effect called reverse rotation, where the intrinsic and orbital rotations are antiparallel. Contrary to what happens in the frictionless case, where steady reverse rotations are possible, we find that this dynamical behavior may exist only as a tran- sient when dissipation is considered. Whether or not reverse rotations in fact occur depende on two parameters, one related to dissipation and in- ertia and the other related to the geometric configuration of the system. The critical value of this geometric parameter (separating the regions where reverse rotation is possible from those where it is forbidden) falls off in a q-exponential way. Calculating the drag on a cylinder in a wind tunnel Paulo Victor Santos Souza Universidade Federal Fluminense (UFF) & Instituto Federal de Educa¸c˜ao, Ciˆencia e Tecnologia do Rio de Janeiro (IFRJ) – Rio de Janeiro – Brazil The Navier-Stokes equations describing the behavior of a fluid flowing. The solution of this equation for most of the problems can not be solved exactly. Therefore, in most cases the numerical approach is the best alter- native to get accurate and reliable results. There are numerous methods developed exclusively to address the problem in a fluid flowing through. Recently [1] the method of finite differences to relaxation, was used to study the problem of a fluid flowing around a cylinder with different val- ues of the Reynolds number. It was possible to verify the formation of mats Von K´arm´an. However, there was calculated the drag force on the cylinder. In this work, we use the finite difference method with relaxation Abstracts: Poster Sessions 91 to compute the drag force on the cylinder. [1] P. M. C. de Oliveira, Relaxation method for navier stokes equation, Inter- national Journal of Modern Physics C 23, 1250021 (2012). Statistical model of impact fragmentation in a disk Rebeca C. Falc˜ao & Fernando Parisio Dpto. de F´ısica, Universidade Federal de Pernambuco (UFPE) – Pernambuco – Brazil In this work was calculated the fragments size distribution of a two- dimensional region with a punctual impact from which cracks originate. We assume the patterns to be built by two simple ingredients: concen- tric circumferences, whose radii assume random values in the interval ]0,R] and semi-infinite straight lines emanating from the center of the circumference, with angles that are also random variables. The radii dis- tribution of circular cracks was achieved by basics concepts of physics such as energy propagation, and the angles distribution of radial cracks was supposed to equal a uniform distribution, because of the system’s simmetry. Statistical complexity and pattern formation in cosmology Reinaldo R. Rosa & D. H. Stalder & C. A. Wuensche & A. L. B. Ribeiro & F. M. Ramos Instituto Nacional de Pesquisas Espaciais (INPE/MCTI) – S˜ao Paulo – Brazil We investigate two important questions about the use of the nonexten- sive thermostatistics formalism in the context of nonlinear galaxy clus- tering and pattern formation in cosmological scales. Firstly, we review a quantitative criterion for justifying nonextensivity at different physical cosmological scales [1]. Then, we discuss the physics behind the ansatz of the entropic parameter q(r). Our results, from both observational and simulated data [2], suggest the approximate range where nonextensivity Abstracts: Poster Sessions 92 can be justified and, hence, give some support to the applicability of q(r) to the study of large-scale structures in cosmology. [1] Wuensche et al., Physica A 344, Issues 3–4: 743–749, (2004); [2] Stalder et al., http://arxiv.org/abs/1208.3444. Scaling law and anti-persistent motion of annihilating defects in a lyotropic liquid crystal 1,2,3, 1,2 1,3 Renato R. Guimar˜aes † & Haroldo V. Ribeiro & Hatsumi Mukai & Paulo R. G. Fernandes1,3 & Rodolfo T. de Souza4 & Ervin K. Lenzi1,2 & Renio S. Mendes1,2 1Departamento de F´ısica, Universidade Estadual de Maring´a (UEM) – Paran´a– Brazil 2National Institute of Science and Technology for Complex Systems (INCT-SC) – Rio de Janeiro – Brazil 3National Institute of Science and Technology for Complex Fluids (INCT-CF) – S˜ao Paulo – Brazil 4Universidade Tecnol´ogica Federal do Paran´a(UTFPR), Campus Pato Branco – Paran´a– Brazil Topological defects can appear whenever there is some type of ordering. Its ubiquity in nature has been the subject of several studies, from early Universe to condensed matter. In this work, we investigated the annihi- lation dynamics of defects and antidefects in a lyotropic nematic liquid crystal (ternary mixture of potassium laurate, decanol and deionized- destilated water) using the polarized optical light microscopy technique for the experimental measures and statistical physics techniques for the data analysis. We analyzed Schlieren textures with topological defects produced due to a symmetry breaking in the transition of the isotropic to nematic calamitic phase after a temperature quench. As result, we obtained for the distance D between two annihilating defects (defect- antidefect pair), as a function of time t remaining for the annihila- tion, the scaling law D tα, with α = 0.390 and standard deviation σ =0.085. This scaling law∝ is in good quantitative agreement with pre- vious investigations on the subject. We further present statistically sig- nificant evidence that the relative velocity between defect pairs is Gaus- sian distributed, anti-persistent and long-range correlated, by using DFA Abstracts: Poster Sessions 93 analysis. Beyond that, we show that simulations of the Lebwohl-Lasher model reproduce quite well our experimental findings related to the anti- persistent behaviour. Our findings go in the direction to extend experi- mental results related to dynamics of defects in liquid crystals since only thermotropic and polymerics ones had been investigated. †Email address: [email protected]. Time-dependent Monte Carlo simulations for the refinement of critical points for extensive and non-extensive spin models Roberto da Silva Universidade Federal do Rio Grande do Sul (UFRGS) – Rio Grande do Sul – Brazil We developed methods to determine critical parameters of the interacting spin systems based on optimization of power laws obtained under suitable initial conditions. For that, we considered the scaling relations obtained from relaxation of magnetic system initially at high temperature which is suddenly quenched to the critical temperature, which became known in statistical mechanics as “short time dynamics”. The difference of our methods in relation to the conventional short-time dynamics is to deter- mine the critical parameters instead of only find the critical exponents when we already have an accurate estimate of the critical parameter from another method used in the equilibrium regime. We will show that our method covers not only extensive systems (q = 1) but also for the models under non-extensive regime (q = 1). We will present results for critical 6 and multicritical points of the several models in Statistical Mechanics. Abstracts: Poster Sessions 94 Bridging stylized facts in finance and data non-stationarities Sabrina Camargo Escola de Matem´atica Aplicada, Funda¸c˜ao Get´ulio Vargas (EMAp/FGV) – Rio de Janeiro – Brazil Employing a recent technique which allows the representation of nonsta- tionary data by means of a juxtaposition of locally stationary paths of different length, we introduce a comprehensive analysis of the key observ- ables in a financial market: the trading volume and the price fluctuations. From the segmentation procedure we are able to introduce a quantitative description of statistical features of these two quantities, which are often named stylized facts, namely the tails of the distribution of trading vol- ume and price fluctuations and a dynamics compatible with the U-shaped profile of the volume in a trading section and the slow decay of the au- tocorrelation function. The segmentation of the trading volume series provides evidence of slow evolution of the fluctuating parameters of each patch, pointing to the mixing scenario. Assuming that long-term features are the outcome of a statistical mixture of simple local forms, we test and compare different probability density functions to provide the long-term distribution of the trading volume, concluding that the log-normal gives the best agreement with the empirical distribution. Moreover, the seg- mentation of the magnitude price fluctuations are quite different from the results for the trading volume, indicating that changes in the statistics of price fluctuations occur at a faster scale than in the case of trading volume. Abstracts: Poster Sessions 95 Analytical solutions for a nonlinear diffusion equation: convection and reaction terms Sergio Curilef Departamento de F´ısica, Universidad Cat´olica del Norte (UCN) – Antofagasta – Chile Exact analytical solutions are proposed for a family of nonlinear diffu- sion equations, which typically appears in nonlinear problems of heat and mass transfer and flows in porous media. A diffusion type solution based on a power law emerges from an ansatz useful to write a set of ordinary coupled equations that is easily solved, allowing to construct its exact solution. The result recovers its linear form as a special limit. Additionally, we apply to problems where it is considered as convection as reaction term. In this latter case, Velhurst growth and global regula- tion is added. Again, a power law solution is proposed to write a couple of ordinary differential equations that are easily solved, allowing to con- struct its exact solution. The equations admit an interpretation in terms of population dynamics and are related to the so-called conserved Fisher equation. In every case, it is possible to set the solution to the Tsallis q-exponentials. Email address: [email protected]. On generalized entropic uncertainty relations for the quNit Steeve Zozor1,2 & G. M. Bosyk2 & M. Portesi2 1Laboratoire Grenoblois d’Image, Parole, Signal et Automatique (GIPSA-Lab, CNRS) – Grenoble – France 2Instituto de F´ısica La Plata (IFLP), Universidad Nacional de La Plata (UNLP), National Research Council (CONICET) – La Plata – Argentina We present entropic formulations of the uncertainty principle satisfied by an arbitrary pair of quantum observables, say A and B, with dis- crete spectra on an N-dimensional Hilbert space (quNit). We use here the R´enyi entropy Hλ to measure the ignorance or lack of information Abstracts: Poster Sessions 96 associated to the probability distribution for the outcome of A and B eigenvalues (resp. pA y pB). In particular, we exhibit a non trivial min- A B imal bound for the sum of the R´enyi entropies Hα(p ) + Hβ(p ) for any nonnegative couple of entropic indices (α, β). In the literature, such bounds are derived, using in general the Riesz-Thorin theorem, that im- poses the indices to be H¨older conjugated (1/α +1/β = 2); with our approach it is possible to go beyond the scope of the Riesz-Thorin theo- rem, allowing to cover all the quadrant for the couple of entropic indices. Our approach is based on two steps: (i) we first minimize the entropy of a probability vector subject to the maximum of this vector; (ii) then, we minimize the sum of the minimum entropies obtained in step (i) subject to the Landau–Pollak inequality that links the maximum of the distribu- tions pA and pB. In this work we solve the problem geometrically, using mainly convexity properties (of the space of probability vectors subject to its maximal component, of the norm to optimize) and the decreasing property of the minimal entropy. It turns out that our bound only de- pends on the overlap c between the eigenvectors of the observables. Two situations are then distinguished versus c: When c> 1 , the problem reduces to that of the qubit (N = 2) we • √2 solved in a recent work [1]. The bound we obtain here is universal (state-independent), and optimal for c fixed; we exhibit pair of observables with this c so that the their exists at least one state that saturate the bound (minimizing state). When c 1 , the problem remains partially open: • ≤ √2 – With this procedure we show that it is not possible to im- prove the known sub-optimal bound evaluated by Maassen- Uffink [2] when α and β are H¨older-conjugated (and more gen- erally for any couple of indices above the conjugation curve), α – When β is larger than 2α 1 (the H¨older-conjugated of α), we show that our bound improve− the bound of Deutch [3], the only one known in this part of the plane (except in some special part of the plane [4]). Recently Puchala et al. derived a bound for the sum of entropies with same index (β = α) that depends on the pair of observables [4]. Due to Abstracts: Poster Sessions 97 the optimality of our bound when c> 1 is fixed, it is obviously higher √2 to the minimal bound of Puchala over the pairs of observables having the same overlap. When c 1 this question remains open, but some, ≤ √2 simulations seem to indicate that again our bound improve the minimal one Puchala when c is fixed. Note finally that there exists a one-to-one mapping between the R´enyi entropy and the Tsallis entropy. Thus, uncertainty inequalities satisfied by the Tsallis entropy can easily be deduced from our inequalities (the sum of the entropy being replaced by a deformed/non extensive sum). Note also that our procedure applies directly to the sum of the Tsallis entropy, allowing to derive uncertainty inequalities using the usual sum of Tsallis entropies. [1] S. Zozor, G. M. Bosyk, M. Portesi, On a generalized entropic uncertainty relation in the case of the qubit, arXiv:1306.0409 [quant-ph] (2013); [2] H. Maassen, J. B. M. Uffink, Generalized entropic uncertainty relations, Physical Review Letters 60, 1103 (1988); [3] D. Deutsch, Uncertainty in quantum measurements, Physical Review Let- ters 50(9), 631–633 (1983); [4] Z. Puchala, L. Rudnicki, K. Zyczkowski, Entropic uncertainty relations and majorization, Journal of Physics A 46(27), 272002 July (2013). Deformed Pythagorean triples and Fibonacci sequences Daniel P. M. Fernandes1 & Suani T. R. Pinho1 & Ernesto P. Borges1 & Thierry C. Petit Lob˜ao2 1Instituto de F´ısica, Universidade Federal da Bahia (UFBA) – Bahia – Brazil 2Instituto de Matem´atica, Universidade Federal da Bahia (UFBA) – Bahia – Brazil There are infinit solutions for the Pythagorean triples, (x,y,z) integers that satisfy zn = xn + yn, with n 2 (n> 2 has no solution, according to the celebrated Fermat’s last theorem≤ recently proved by A. Wyles). We use the deformed addition operator a, defined as x a y = x + y + axy (deformed addition is frequent to⊕ appear as a =⊕ 1 q), and computationally search for solutions for the Diophantine equation− zn = Abstracts: Poster Sessions 98 n n x a y . Despite the known result a = 0, we have observed that this generalized⊕ version, in each power n, has at least a trivial solution (1, 1, 2) for the case a = 2n 2. Moreover we have found that the number of − solutions, in each power n, is very scarce for a > 0. For instance, for 2 A family of Leibniz triangles as models for correlated systems Thierry C. Petit Lob˜ao1 & Suani T. R. Pinho2 & Ernesto P. Borges2 & Constantino Tsallis3 1Instituto de Matem´atica, Universidade Federal da Bahia (UFBA) – Bahia – Brazil 2Instituto de F´ısica, Universidade Federal da Bahia (UFBA) – Bahia – Brazil 3Centro Brasileiro de Pesquisas F´ısicas (CBPF) – Rio de Janeiro – Brazil Many natural systems are well described by Gaussian probability distri- butions in the thermodynamic limit, provided that the N random vari- ables are independent or weakly correlated. According with de Moivre- Laplace theorem, the distribution in a Bernouilli process is a Gaussian distribution in this limit. On the other hand, Leibniz triangles, also multiplied by Pascal coefficients, generate uniform distribution, that is Abstracts: Poster Sessions 99 identified with a q-Gaussian as q . All triangles obey the Leibniz → −∞ rule, for which the sum of successive elements rN,n at position n and n +1 of line N corresponds to the element n in line N 1 in order to en- − sure the total symmetry of micro-states. For triangles given by Bernoulli N N n n trials, rN,0 = p and rN,n = p − (1 p) , with p and 1 p as the probability of independent variable. For− Leibniz triangles, besides− the Leibniz rule, the boundary conditions are rN,0 = 1/(N + 1). A general- ization of Leibniz triangles was proposed to generate a family of corre- lated systems described by a q-Gaussian with q < 1 (A. Rodr´ıguez, V. Schw¨ammle, C. Tsallis, J. Stat. Mech., P09006 (2008)). For generalized Leibniz triangles with a parameter ν, such that the boundary conditions (ν) are rN,n = B(n + ν,N + ν n)/B(ν,ν), in which B(X,Y ) stands for the Beta function, Rodriguez −et al. have obtained analytically and numeri- cally q-Gaussian distributions for q = (ν 2)/(ν 1). Note that, when − − ν = 1 and n = 0, the Leibniz triangles are recovered. In this work, we consider a family of Leibniz triangles to generate q-Gaussian distributions with q > 1 (R. Hanel, S. Thurner, C. Tsallis, EPJ B 72, 263 (2009)). In this case, the boundary conditions are such that ν =1/2, 3/2,...; for (1/2) 2 2N 1 ν = 1/2, we have rN,0 = (2N 1)!/ N[(N 1)!] 2 − . We expect to find q-Gaussian distributions− with q{=(3+2−ν)/(1+2ν)} according to Hanel et al.. Electronic transport through disordered wires using Stochastic Differential Equations Victor Pedrosa & Antˆonio M. S. Macˆedo Universidade Federal de Pernambuco (UFPE) – Pernambuco – Brazil Electronic transport through a disordered wire is one of the fundamental problems in mesoscopic physics. Dorokhov (1982) and (independently) Mello, Pereyra, and Kumar (1988) developed a theory to describe the evolution of the distribution function P (λ1,λ2,...,λN ,L) with increasing wire length, where λi is related to the transmission eigenvalue Ti of the multimode wire through λ = (1 T )/T . The DMPK equation i − i i ∂P 2 N ∂ ∂ P l = λ (1 + λ )J ∂L βN +2 β ∂λ n n ∂λ J n=1 n n − X Abstracts: Poster Sessions 100 N N J = λ λ β | j − i| i=1 j=i+1 Y Y is a Fokker-Planck equation and an exact solution to that is only know for the case β = 2. The results for this equation, in most of the cases, have been obtained for the asymptotic cases L or N . However, the transport properties of systems with a→ finite ∞ number→ of ∞ propagating modes are still not well understood. We also notice that there is a lack in the literature of a general approach to achieve the solutions for all the ten classes of DMPK equations. Here we propose to rewrite the DMPK equation as an equivalent Itˆo Stochastic Differential Equation. With this approach we can achieve the metallic (diffusive) regime, the localised regime or the crossover (between metallic and localised) regime. We can also easily change among (at least) seven of the ten classes of DMPK equations. Using the SDE version of the DMPK equation, we numerically solved it and showed how P (ln(λ1),L) evolves with increasing wire length from a del ta peak around zero to a Gaussian distribution as we approach the localised regime. We also showed that the same does not happen for the BdG class without spin- reverse symmetry (as expected). Cellular Automata simulation of people moving in confined space in the presence of obstacles Wellington P. A. Spinola & J´essica Souto Santana & Igino de Oliveira Silva J´unior & Carlos Felipe S. Pinheiro & Everaldo Arashiro & Alcides Castro e Silva Universidade Federal de Ouro Preto (UFOP) – Minas Gerais – Brazil The subject of our work is to study the behaviour os people trying to leave a confined space using some limits exits. In situations where panic took place, is it common to observe how this dynamic became extremely disorganized. Although such phenomena have many causes based in Hu- man Nature, there are many others factors feasible to study. By physical Abstracts: Poster Sessions 101 methods including computer simulations. Many people moving and inter- acting themselves together is an exemple of a highly complex system,and, this way cannot be modelad as a sum of the Independent movements of single persons. The interaction among particles, in this case of people, is the main causes of the emergence of patterns that we are interested. In order to simulate such problem we discretized the room in cells and use cellular automata under some rules in order to establish the dynamic. Ba- sically we model people as particles traped in a discretized container (i.e. A Room) and the rules of movements are taken under the influence of a “Floor Field” created using Manhattan distances to the exits. We apply the model in a case study of a seminar room located at ICEB/UFOP. We study then how the number, the disposition and the size of the exits af- fect the time necessary to take all the people out of the room. Supported by Capes, CNPq and Fapemig. Participants Name Institution Country Airton Deppman USP/S˜ao Paulo Brazil AlbertoRobledo UNAM/MexicoCity Mexico AlessandroPluchino UNICT/Italy Italy AlexB.deFigueiredo UFF/RiodeJaneiro Brazil AlexandreSoutoMartinez USP/S˜aoPaulo Brazil AllbensP.F.Atman CEFET/MinasGerais Brazil AlysonPauloSantos UFRN/RioGrandedoNorte Brazil Andr´eMaur´ıcioC.deSouza UFS/Sergipe Brazil AndreaRapisarda UNICT/Italy Italy AndresM.Kowalski UNLP/LaPlata Argentina AndresR.R.Papa ON/RiodeJaneiro Brazil Angel Akio Tateishi UEM/Paran´a Brazil AngelPlastino UNLP/LaPlata Argentina AngelRicardoPlastino UNNOBA/BuenosAires Argentina AnnaChame UFF/RiodeJaneiro Brazil AnnaPaulaR.Bacalhau CBPF/RiodeJaneiro Brazil AntonioConiglio Univ.ofNaplesFedericoII Italy AntonioRodr´ıguezMesas UPM/Spain Spain Apiano Morais URCA/Cear´a Brazil Armando Prestes M. Filho SINTEF Brasil/Rio de Janeiro Brazil BeneditoJ.C.Cabral ULisboa/Lisboa Portugal Bernardo C. C. dos Santos PETROBRAS/Rio de Janeiro Brazil Bruce M. Boghosian AUA/Yerevan Armenia BrunoG.daCosta IFSert˜ao-PE/Pernambuco Brazil CarlosHenriqueBrandt CBPF/RiodeJaneiro Brazil CeliaB.Anteneodo PUC-Rio/RiodeJaneiro Brazil Cesar Ivan Nunes S. Filho UFC/Cear´a Brazil ChristianoJ.G.Pinheiro UFES/Vit´oria Brazil ConstantinoTsallis CBPF/RiodeJaneiro Brazil CrysttianArantesPaix˜ao FGV/RiodeJaneiro Brazil DanielAdri´anStariolo UFRGS/RioGrandedoSul Brazil DanielBritodeFreitas UFRN/RioGrandedoNorte Brazil Diego Mateos UNC/C´ordoba Argentina EdsondeP.daSilva UFRRJ/RiodeJaneiro Brazil continue on next page Participants 103 Name Institution Country EltonJos´edaSilvaJ´unior UFMG/MinasGerais Brazil EricoR.PereiradeNovais CBPF/RiodeJaneiro Brazil ErnestoP.Borges UFBA/Bahia Brazil ErvinKaminskiLenzi UEM/Paran´a Brazil Eugenio E. Vogel UFRO/Temuco Chile EvaldoM.FleuryCurado CBPF/RiodeJaneiro Brazil FabianoLemesRibeiro UFLA/MinasGerais Brazil FelipeA.SeverinodosSantos UFOP/MinasGerais Brazil Felipe E. Olivares Zamora UNLP/La Plata Argentina FelipeMondaini CEFET/RiodeJaneiro Brazil FelipeT.L.Germani CBPF/RiodeJaneiro Brazil FernandoDantasNobre CBPF/RiodeJaneiro Brazil Fernando Jos´eAntˆonio UEM/Paran´a Brazil Flavia Pennini UCN/Antofagasta Chile Fl´avio Santana Michels UEM/Paran´a Brazil FortunatoSilvadeMenezes UFLA/MinasGerais Brazil FranciscoRocha UFPE/Pernambuco Brazil G.CigdemYalcin IstanbulUniversity Turkey GabrielAlvesMendes UFC/Cear´a Brazil GabrielDiasCarvalho UFPE/Pernambuco Brazil GabrielaAlineCasas CBPF/RiodeJaneiro Brazil GabrielleSallerNornberg IMPA/RiodeJaneiro Brazil Georgios P. Pavlos DUTH/Thrace Greece Gokhan Baris Bagci Ege University/Ismir˙ Turkey GuiomarRuizLopez UPM/Spain Spain Hans Herrmann ETH/UFC/Cear´a Switzerland HenrikJeldtoftJensen ImperialCollegeLondon UK HirokiSuyari ChibaUniversity Japan IvanoDami˜aoSoares CBPF/RiodeJaneiro Brazil Jan Naudts University of Antwerp Belgium JefersonJacobArenzon UFRGS/RioGrandedoSul Brazil Jes´usS´anchez-Dehesa UGR/Granada Spain Jo˜aoVitorM.deMiranda USP/S˜aoPaulo Brazil Jo˜ao Vitor N. Fontana UFPE/Pernambuco Brazil Jo˜aoRibeiroMedeiros CBPF/RiodeJaneiro Brazil Jos´eA C. Nogales UFLA/Minas Gerais Brazil Jos´eE.P.deCarvalho CBPF/RiodeJaneiro Brazil Jos´eGlaucoR.Tostes UENF/RiodeJaneiro Brazil Jos´eSoares de Andrade Jr. UFC/Cear´a Brazil continue on next page Participants 104 Name Institution Country Jos´eWashington dos Santos UNB/Distrito Federal Brazil Jos´eWeberszpil UFRRJ/RiodeJaneiro Brazil KarenLuzBurgoa-Rosso UFLA/MinasGerais Brazil LeandroPradeNadaletti COPPE/UFRJ Brazil LeonardoJ.L.Cirto CBPF/RiodeJaneiro Brazil LeonardoO.P.Rosas CBPF/RiodeJaneiro Brazil Leonidas P. Karakatsanis DUTH/Thrace Greece Liacir dos Santos Lucena UFRN/Rio Grande do Norte Brazil LucianaA.Rios CBPF/RiodeJaneiro Brazil LucianoR.daSilva UFRN/RioGrandedoNorte Brazil LudianeSilvaLima UERJ/RiodeJaneiro Brazil LuisCesarPassoni UENF/RiodeJaneiro Brazil LuizGustavodeA.Alves UEM/Paran´a Brazil Maike A. F. dos Santos UEM/Paran´a Brazil Marcel Ausloos ULg/Li`ege Belgium MarceloByrroRibeiro UFRJ/RiodeJaneiro Brazil MarceloLobatoMartins UFV/MinasGerais Brazil MarciaC.Barbosa UFRGS/RioGrandedoSul Brazil MarcioA.F.deMenezes UFF/RiodeJaneiro Brazil MarcoAntonioAmaral UFMG/MinasGerais Brazil MarcoA.RegoMonteiro CBPF/RiodeJaneiro Brazil Maria C. de Sousa Vieira Thomson Reuters/California USA Maur´ıciodeSousaRibeiro CBPF/RiodeJaneiro Brazil Maury Duarte Correa Petrobras/CBPF/Rio de Janeiro Brazil MaxJ.J´aureguiRodr´ıguez CBPF/RiodeJaneiro Brazil MichaelMoraesCˆandido PUC-Rio/RiodeJaneiro Brazil MirellaSim˜oesSantos UFRJ/RiodeJaneiro Brazil Nikos Kalogeropoulos WCMC-Q/Doha Qatar NiloBarrantesMelgar CBPF/RiodeJaneiro Brazil Norma Canosa UNLP/La Plata Argentina Osvaldo Anibal Rosso UFAL/Alagoas Brazil PabloSouzadeCastroMelo UFPE/Pernambuco Brazil Paul Bourgine Ecole´ Polytechnique/Paris France Paula dos S. Marcondes UTFPR/Paran´a Brazil PauloMuriloC.deOliveira UFF/RiodeJaneiro Brazil Paulo Victor Santos Souza UFF/IFRJ/Rio de Janeiro Brazil RaulOscarVallejos CBPF/RiodeJaneiro Brazil Ra´ul Rossignoli UNLP/La Plata Argentina RebecaCardimFalcao UFPE/Pernambuco Brazil continue on next page Participants 105 Name Institution Country ReinaldoR.Rosa INPE/S˜aoPaulo Brazil RenatoRibeiroGuimar˜aes UEM/Paran´a Brazil ReniodosSantosMendes UEM/Paran´a Brazil RobertodaSilva UFRGS/RioGrandedoSul Brazil RobertoF.S.Andrade UFBA/Bahia Brazil RogerMaynard UJF/Grenoble France RonaldDickman UFMG/MinasGerais Brazil RosaneRiera PUC-Rio/RiodeJaneiro Brazil RoseliS.Wedemann UERJ/RiodeJaneiro Brazil RudolfHanel MUV/Vienna Austria Sabir Umarov University of New Haven USA SabrinaCamargo FGV/RiodeJaneiro Brazil Sergio Curilef UCN/Antofagasta Chile S´ergioGalv˜aoCoutinho UFPE/Pernambuco Brazil SergioMartinsdeSouza UFLA/MinasGerais Brazil S´ılvioC.Ferreira UFV/MinasGerais Brazil S´ılvioM.DuarteQueir´os CBPF/RiodeJaneiro Brazil SilvioR.A.Salinas USP/S˜aoPaulo Brazil SolangeG.F.Martins UFLA/MinasGerais Brazil Steeve Zozor GIPSA-lab/CNRS France StefanThurner MUV/Vienna Austria SuaniT.R.Pinho UFBA/Bahia Brazil SuzanaMossdeOliveira UFF/RiodeJaneiro Brazil SylvioCanuto USP/S˜aoPaulo Brazil Tania P. Sim˜oes Yamaki UNICAMP/S˜ao Paulo Brazil Thiago de Melo Santiago UFC/Cear´a Brazil ThierryC.PetitLob˜ao UFBA/Bahia Brazil TobiasMicklitz CBPF/RiodeJaneiro Brazil Ugur Tirnakli Ege University/Ismir˙ Turkey VicenteA.A.Espinoza PUC-Rio/RiodeJaneiro Brazil Victor P. Braga Cavalcanti UFPE/Pernambuco Brazil WellingtonP.A.Spinola UFOP/MinasGerais Brazil Wemerson P. O. Marinho JGP Gest˜ao Global de Recursos Brazil YuriJacobLumer IBMEC/RiodeJaneiro Brazil Constantino Tsallis Constantino Tsallis was born in Athens-Greece, grew up in Argentina, and acquired the Brazilian citizenship since 1981. He works in the area of statistical mechanics, and presently heads the National Institute of Science and Technology for Complex Systems of Brazil. He obtained his title of Docteur d’Etat´ `es Sciences Physiques from the University of Paris- France in 1974. He has worked in a variety of theoretical subjects in the areas of critical phenomena, chaos and nonlinear dynamics, economics, cognitive psychology, immunology, population evolution, among others. Since over two decades, he is focusing on the entropy and the foundations of statistical mechanics, as well as on some of their scientific and techno- logical applications. Indeed, he proposed in 1987 and formally published in 1988 a generalization of the Boltzmann-Gibbs entropy and its associ- ated statistical mechanics. This generalization is presently being actively studied around the world: a Bibliography containing more than 4,000 di- rectly related articles, by more than 6,000 scientists from all over the world, is available at http://tsallis.cat.cbpf.br/biblio.htm. Prof. Tsallis’ contributions have received over 13,000 ISI citations (more than 3,000 of them for his 1988 paper), which currently makes him one among the most cited scientists of all times in Latin America. He has received many international and national distinctions (Guggenheim Foundation Award, Mexico Prize for Science and Technology, Rio de Janeiro Prize of Science and Technology, among many others), and has been given in four occasions the title of Doctor Honoris Causa by Universities from Ar- gentina (Cordoba), Brazil (Maringa and Natal) and Greece (the Thessa- loniki Aristotelian University). He is member of the Academy of Sciences of Brazil, as well as of the Academy of Economical, Political and Social Sciences of Brazil. He received in 2012 the highest distinction from the Academy of Athens. He is main editor of Physica A – Elsevier (Amster- dam), and has supervised close to 40 Doctor and Master Thesis. He has given regular undergraduate and graduate courses in Physics in Brazil, Argentina, USA, France and Germany, and has given over 900 invited lectures around the world. Prof. Tsallis is an external Professor of the Santa Fe Institute, New Mexico. Notes Notes 108 Notes 109 Notes 110 Notes 111 Notes 112 Notes 113 Notes 114 Notes 115 Notes 116